Dr. Fuji's research crew found a pregnant Mew in Guyana and brought her to Cinnabar Mansion. The Mew gave birth to Mewtwo on February 6.
The research team subjected Mewtwo to genetic splicing experiments until he rampaged throughout Cinnabar Mansion and escaped.
Giovanni found Mewtwo later and offered to help him focus his powers. In reality, Mewtwo ended up doing Team Rocket's dirty work in snatching up wild Pokémon for the grunts.
As soon as Mewtwo found out Giovanni sees him as a slave, he angrily breaks out of the Team Rocket hideout and hid in Cerulean Cave.
Mewtwo initially didn't trust humans from that point until Leaf caught and befriended him.