"I am Mewtwo, the world's most powerful Pokémon." –Mewtwo

I hope this quote inspired you to give your Mewtwo a great moveset as much as it did me.
Okay, so I have 3 seperate movesets: two for each Mega Evo and one if you're playing in Gen 5 or earlier.
Mega Mewtwo X @ Mewtwonite X

Ability: Pressure --> Steadfast
Jolly Nature
EVs: 252 Atk / 252 Spd / 4 HP
- Brick Break
- Psycho Cut
- Earthquake
- Poison Jab
The first two are STAB moves that have good coverage by themselves. Earthquake has great power and coverage, and Poison Jab just became great for killing Fairies.
Mega Mewtwo Y @ Mewtwonite Y

Ability: Pressure --> Insomnia
Timid Nature
EVs: 252 SpA / 160 Spd / 100 HP
- Psystrike
- Aura Sphere
- Ice Beam
- Thunderbolt
Psystrike is a STAB move that does physical damage (nice since Pokémon that are weak to Psychic often have good Special Defense). Aura Sphere is good for Dark-types, as well as many others. And of course, Mewtwo gets the BoltBeam combo.
Mewtwo @ Expert Belt
Ability: Pressure
Timid Nature
EVs: 252 SpA / 252 Spd / 4 HP
- Psystrike
- Aura Sphere
- Ice Beam
- Thunderbolt
Since both Mewtwo and Mega Mewtwo Y are special attackers, they have the same moveset. Note that the held item and EVs are different, though.
So there you go. Mewtwo is a great competitive Pokémon, as its Mega form is
the most powerful in the entire game. I hope you liked it, and if you did or have anything to say, feel free to leave a vote/comment.