The moves Hydro Cannon, Blast Burn, and Frenzy Plant are exclusive moves available only to the starter Pokémon of the corresponding type (Typhlosion for Blast Burn, Samurott for Hydro Cannon, Venusaur for Frenzy Plant, etc.).
Since Mew is not a starter Pokémon, he cannot learn these moves. Simple.
Theoretically, yes, Mew should be able to lear these moves. However, this would corrupt the logic of the games (if that even exists), so Game Freak decided to not let Mew in on the moves.