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Mew can't learn certain moves such as Hydro Cannon, what are the other moves Mew cannot learn?

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Anything that isnt a move tutor, tm or hm. Really long list.

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I'm working on a full list of all of Mew's impossible moves. Some of the moves I've included are only possible in a previous generation, but since transferring it over to a new game is possible it is 100% possible to have those moves.

-Absorb
-Acid
-Acid Armour
-Acid Spray
-Acupressure
-Aeroblast
-Agility
-Air Cutter (but possible in gen 4 via move tutor)
-Air Slash
-Ally Switch (but possible in gen 5 via tm)
-Aqua Jet
-Aqua Ring
-Arm Thrust
-Aromatherapy
-Aromatic Mist
-Assist
-Assurance
-Astonish
-Attack Order
-Aurora Beam
-Autotomize
-Avalanche (but possible in gen 4 via tm)
-Baby-Doll Eyes
-Barrage
-Beat Up
-Belch
-Belly Drum
-Bestow
-Bide
-Bite
-Blast Burn
-Blaze Kick
-Blue Flare
-Body Slam (but possible in gen 3 via move tutor)
-Bolt Strike
-Bone Club
-Bone Rush
-Boomerang
-Boom Burst
-Brave Bird
-Brine (but possible in gen 4 via tm)
-Bubble
-Bubble Beam
-Bug Buzz
-Bullet Punch
-Bullet Seed (but possible in gen 4 via tm)
-Camouflage
-Captivate (but possible in gen 4 via tm)
-Celebrate
-Charge
-Charm
-Chatter
-Chip Away
-Circle Throw
-Clamp
-Clear Smog
-Close Combat
-Coil
-Comet Punch
-Confuse Ray
-Confusion
-Constrict
-Conversion
-Conversion 2
-Copycat
-Cosmic Power
-Cotton Guard
-Cotton Spore
-Counter (but possible in gen 3 via move tutor)
-Crabhammer
-Crafty Shield
-Cross Chop
-Cross Poison
-Crunch
-Crush Claw
-Crush Grip
-Curse
-Dark Void
-Defend Order
-Defence Curl (but possible in gen 3 via move tutor)
-Defog (but possible in gen 4 via tm)
-Destiny Bond
-Detect
-Diamond Storm
-Disable
-Disarming Voice
-Discharge
-Dizzy Punch
-Doom Desire
-Double Hit
-Double Kick
-Double Slap
-Double-Edge (but possible in gen 3 via move tutor)
-Draco Meteor
-Dragon Ascent
-Dragon Breath
-Dragon Dance
-Dragon Rage
-Dragon Rush
-Draining Kiss
-Drill Peck
-Dynamic Punch (but possible in gen 3 via move muter)
-Eerie Impulse
-Egg Bomb
-Electric Terrain
-Electrify
-Electro Ball
-Ember
-Encore
-Entrainment
-Eruption
-Extrasensory
-Extreme Speed
-Fairy Lock
-Fairy Wind
-Fake Tears
-Feather Dance
-Feint
-Fell Stinger
-Fiery Dance
-Final Gambit
-Fire Fang
-Fire Pledge
-Fire Spin
-Fissure
-Flail
-Flame Burst
-Flame Wheel
-Flare Blitz
-Flatter
-Flower Shield
-Flying Press
-Focus Energy
-Follow Me
-Force Palm
-Foresight
-Forest's Curse
-Freeze Shock
-Freeze Dry
-Frenzy Plant
-Fury Attack
-Fury Cutter (but possible in gen 4 via move tutor)
-Fury Swipes
-Fusion Bolt
-Fusion Flare
-Future Sight
-Gear Grind
-Geomancy
-Glaciate
-Glare
-Grass Pledge
-Grass Whistle
-Grassy Terrain
-Gravity
-Growl
-Growth
-Grudge
-Guard Split
-Guard Swap
-Guillotine
-Gust
-Hammer Arm
-Happy Hour
-Harden
-Haze
-Head Charge
-Head Smash
-Headbutt (but possible in gen 4 via move tutor)
-Heal Block
-Heal Order
-Heal Pulse
-Healing Wish
-Heart Stamp
-Heart Swap
-Heat Crash
-Heavy Slam
-Hex
-High Jump Kick
-Hold Back
-Hold Hands
-Horn Attack
-Horn Drill
-Horn Leech
-Howl
-Hurricane
-Hydro Cannon
-Hydro Pump
-Hyper Fang
-Hyperspace Fury
-Hyperspace Hole
-Ice Ball
-Ice Burn
-Ice Fang
-Ice Shard
-Icicle Crash
-Icicle Spear
-Imprison
-Inferno
-Ingrain
-Ion Deluge
-Judgment
-Jump Kick
-Karate Chop
-Kinesis
-King's Shield
-Knock Off
-Land's Wrath
-Lava Plume
-Leaf Blade
-Leaf Storm
-Leaf Tornado
-Leech Life
-Leech Seed
-Leer
-Lick
-Light Of Ruin
-Lock on
-Lovely Kiss
-Lucky Chant
-Lunar Dance
-Luster Purge
-Mach Punch
-Magical Leaf
-Magma Storm
-Magnet Bomb
-Magnetic Flux
-Magnitude
-Mat Block
-Mean Look
-Meditate
-Mega Drain
-Mega Kick (but possible in gen 3 via move tutor)
-Mega Horn
-Memento
-Metal Burst
-Metal Claw
-Metal Sound
-Meteor Mash
-Milk Drink
-Mimic (but possible in gen 3 via move tutor)
-Mind Reader
-Minimize
-Miracle Eye
-Mirror Coat
-Mirror Move
-Mirror Shot
-Mist
-Mist Ball
-Misty Terrain
-Moonblast
-Moonlight
-Morning Sun
-Mud Bomb
-Mud Shot
-Mud Sport
-Mud Slap (but possible in gen 4 via move tutor)
-Muddy Water
-Mystical Fire
-Natural Gift (but possible in gen 4 via tm)
-Needle Arm
-Night Wave
-Night Slash
-Noble Roar
-Nuzzle
-Oblivion Wing
-Octazooka
-Odour Sleuth
-Ominous Wind (but possible in gen 4 via move tutor)
-Origin Pulse
-Outrage
-Parabolic Charge
-Parting Shot
-Pay Day
-Peck
-Perish Song
-Petal Blizzard
-Petal Dance
-Phantom Force
-Pin Missile
-Play Nice
-Play Rough
-Pluck (but possible in gen 5 via tm)
-Poison Fang
-Poison Gas
-Poison Tail
-Powder
-Powder Snow
-Power Gem
-Power Split
-Power Swap
-Power Whip
-Precipice Blades
-Present
-Psybeam
-Psycho Boost
-Psycho Cut
-Psycho Shift
-Psystrike
-Psywave
-Punishment
-Pursuit
-Qucik Attack
-Quick Guard
-Quiver Dance
-Rage
-Rage Powder
-Rapid Spin
-Razor Leaf
-Razor Shell
-Razor Wind
-Recover
-Refresh
-Relic Song
-Revenge
-Reversal
-Roar Of Time
-Rock Blast
-Rock Climb (but possible in gen 4 via hm)
-Rock Throw
-Rock Wrecker
-Rolling Kick
-Rollout (but possible in gen 4 via move tutor)
-Rototiller
-Sacred Fire
-Sacred Sword
-Sand Attack
-Sand Tomb
-Scary Face
-Scratch
-Screech
-Searing Shot
-Secret Sword
-Seed Flare
-Seismic Toss (but possible in gen 3 via move tutor)
-Self-Destruct
-Shadow Force
-Shadow Punch
-Shadow Sneak
-Sharpen
-Sheer Cold
-Shell Smash
-Shift Gear
-Silver Wind (but possible in gen 4 via tm)
-Simple Beam
-Sing
-Sketch
-Sky Uppercut
-Slack Off
-Slam
-Slash
-Sleep Powder
-Sludge
-Smelling Salts
-Smog
-Smokescreen
-Soak
-Sonic Boom
-Spacial Rend
-Spark
-Spider Web
-Spike Cannon
-Spikes
-Spikey Shield
-Spit Up
-Spore
-Steam Eruption
-Steamroller
-Sticky Web
-Stockpile
-Stomp
-Stored Power
-Storm Throw
-String Shot (but possible in gen 4 via move tutor)
-Struggle (this move can only be used if the PP of all other moves are gone. There is no way to actually have it learnt as a true move, however)
-Stun Spore
-Submission
-Sucker Punch (but possible in gen 4 via move tutor)
-Supersonic
-Swallow
-Sweet Kiss
-Sweet Scent
-Swift (but posible in gen 4 via move tutor)
-Sweet Scent
-Switcheroo
-Synchronize
-Tackle
-Tail Glow
-Tail Slap
-Tail Whip
-Take Down
-Techno Blast
-Teeter Dance
-Telekinesis (but possible in gen 5 via move tutor)
-Teleport
-Thousand Arrows
-Thousand Waves
-Thrash
-Thunder Shock
-Tickle
-Topsy-Turvy
-Toxic Spikes
-Tri Attack
-Trick-Or-Treat
-Triple Kick
-Trump Card
-Twineedle
-Twister (but possible on gen 4 via move tutor)
-V-Create
-Vaccuum Wave (but possible in gen 4 via move tutor)
-Venom Drench
-Vice Grip
-Vine Whip
-Vital Throw
-Volt Tackle
-Wake-Up-Slap
-Water Gun
-Water Pledge
-Water Shuriken
-Water Sport
-Water Sprout
-Weather Ball
-Whirlpool (but possible in gen 4 via hm)
-Whirlwind
-Wide Guard
-Wing Attack
-Wish
-Withdraw
-Wood Hammer
-Work Up (but possible in gen 5 via tm)
-Wrap
-Wring Out
-Yawn

Source. Looked through the list at every move to check if Mew can learn it.

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edited by
Mew can actually legitimately learn both Pay Day and Bubble Beam in Generation 1. TM 11 Bubble Beam is your reward for beating Mysty the second gym leader of Red and Blue. TM 16 Pay Day can be obtained in Red Blue and Yellow on Route 12 south of Lavender Town. Surf is required to obtain the TM. Oh almost forgot TM 34 in Generation 1 which is the reward for beating Brock is Bide. Apparently Mew can also learn Curse in Generation 2 via TM 3 which is located in the Celadon Condominiums where you get the Tea item in Firered and Leafgreen.

Oh can't forget about TM 24 which is Dragon Breath in Generation 2 which is given to you when you kick Clairs' butt. Dragon Rage is TM 23 in Generation 1 which is purchased at the Game Corner for 3300 coins. Damn yet another mistake. TM 37 is Egg Bomb in Generation 1 Red Yellow and Blue. It is found laying on the ground in the Safari Zone or can be purchased for 2000 poké at the Celadon Dept. store.

Okay you get the point now. If you took the time to look up your answers yourself you'd know TM 27 in Generation 1 is Fissure which is obtained by beating Boss Rocket Giovanni during the final gym battle. TM 49 is Fury Cutter in Generation 2 and is given to you by Bugsy. There are probably several more mistakes in the answer you accepted but its 4AM right now and I'm tired of fixing their mistakes.
You made several mistakes with your answer. I took the liberty of fixing some of them. Next time do your research before you answer a question.
@Akuma625
What exactly are you referring too? You have not done any liberty of fixing the answer, nor do you have the ability to do so. Unless of course, you're probably referring to an answer you have posted that has yet to be approved by a mod.
Edit: Yes, this seemed to be the case

It is another thing though, to accuse a user for not doing their research on a post last updated 4 years ago.
Edit: I see I was wrong
Approved it, sorry for the couple hour discrepancy with this. I moved the post to a comment because it does not answer the question alone.
You probably already saw this but here's what I fixed.

Mew can actually legitimately learn both Pay Day and Bubble Beam in Generation 1. TM 11 Bubble Beam is your reward for beating Mysty the second gym leader of Red and Blue. TM 16 Pay Day can be obtained in Red Blue and Yellow on Route 12 south of Lavender Town. Surf is required to obtain the TM. Oh almost forgot TM 34 in Generation 1 which is the reward for beating Brock is Bide. Apparently Mew can also learn Curse in Generation 2 via TM 3 which is located in the Celadon Condominiums where you get the Tea item in Firered and Leafgreen.

Oh can't forget about TM 24 which is Dragon Breath in Generation 2 which is given to you when you kick Clairs' butt. Dragon Rage is TM 23 in Generation 1 which is purchased at the Game Corner for 3300 coins. Damn yet another mistake. TM 37 is Egg Bomb in Generation 1 Red Yellow and Blue. It is found laying on the ground in the Safari Zone or can be purchased for 2000 poké at the Celadon Dept. store.

Okay you get the point now. If you took the time to look up your answers yourself you'd know TM 27 in Generation 1 is Fissure which is obtained by beating Boss Rocket Giovanni during the final gym battle. TM 49 is Fury Cutter in Generation 2 and is given to you by Bugsy. There are probably several more mistakes in the answer you accepted but its 4AM right now and I'm tired of fixing their mistakes.