In the vide games, in the generation I games of Red, Blue and Yellow.
If your talking about the TV series, it appeared in the first movie: 'Mewtwo Strikes Back' and in the episode where Giovanni uses it to battle Gary's Arcanine and Nidoking. I think.
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Mewtwo is made by scientists with DNA from Mew. Mewtwo wants to be the one and only him, so he wants to find Mew and destroy him, so they will only know Mewtwo from then on. This whole story is found in the first Pokémon movie: "Mewtwo vs. Mew"
Mewtwo is the ultimate Psychic type legendary Pokemon. It was introduced in the first generation and does not evolve into any other Pokemon, although as of the sixth generation it can mega evolve into Mega Mewtwo X or Mega Mewtwo Y.
POKEMON:THE FIRST MOVIE reveals that Mewtwo is much more powerful than any pokemon,even Mew. I agree Mewtwo would beat Mew anytime.
Mew and Mewtwo. Watch the first movie
Mewtwo cannot breed with any Pokémon including Mew. The logic behind it is first its a Legendary and its a clone.