According to an official promotional video, Mewtwo is expected to be found during a limited time event in Pokemon Go. During this event, trainers will be fighting Mewtwo in groups of up to 20 people called Raid Battles. When successfully defeated, everyone who participated in the Raid Battle will have the oppurtunity to capture Mewtwo with special premier balls.
Being a Pure Psychic-type, Mewtwo is only weak to 3 attack types namely: Dark, Ghost and Bug. Use Pokemon with these types of attacks to defeat Mewtwo as quickly as possible. On the other hand, avoid using Fighting and Psychic-type attacks when fighting Mewtwo, as he is resistant to these types of attacks.
Best Pokemon to Beat
Mewtwo has an extremely high attack stat, and by "extremely high" I mean the current best attack stat in the game with no pokemon even coming close. So unless you bring pokemon resistant to Psychic-type attacks your Pokemon will be dropping dead like flies. And even then, that might still not be enough as Mewtwo also has different attack types which are powerful on their own and may deal super effective damage to your Psychic resistant Pokemon.