What are the best moves to teach a mewtwo in Pokemon Diamond?

He is psychic, so you need to defend against his weaknesses. So you need a way to block Bug, Ghost, and Dark. Flamethrower and Ice Beam take out Bug as well as the somewhat invincible Dragon, Dark is weak to Fighting and Bug. And Ghost is weak against Ghost and Dark, but Fighting doesn’t hit Ghost. So choose wisely on the moves. Aura Sphere is okay, I guess. 😛

Easy, Psychic, Aura Sphere, Thunderbolt and Flamethrower
But Ice Beam is good too

1)Basically, Mewtwo fears Bug and Dark types so give it something like Brick Break(Can also destroy pesky defences like Light Screen) and yes, flamethrower and ice beam are good for killing the irritating Bugs, and are generally able to k.o many other types. Try Calm Mind as well.
2)Aura sphere is quite strong an never misses so go for it.
Hope it helps!

my mewtwo knows -calm mind, thunderbolt, psychic and aura sphere

i have a level 100 Mewtwo and these are its moves:
aura sphere
thunderbolt
psychic
hyper beam
however im thinking of removing hyper beam and teaching him shadow ball.

OK, I had the best team with a Mewtwo! But i unfortunately I trade it for a Mew. Well I think i remember that I had this fallowing moves for Mewtwo:
Psychic
Recover
Earthquake
Aura Sphere
Well does moves I think my Mewtwo had, i remember that with does moves I was almost invisible!
Well Psychic is very effective on most types of the Pokemon!
Earthquake is the best move that they can have, because most Pokemon in the game that are attacked by Earthquake die at the First or Second time they do it!
Aura Sphere is very effective, and has the best percentage one hitting a KO Attack!
Recover is just to make sure that Mewtwo dosen´t die very quick and can put up a good fight!
Hope I´d help!