Dr. Fuji's obsession with cloning began after his daughter Amber died. Unable to accept her loss, he poured everything into perfecting cloning technology, convinced he could bring her back. His wife couldn't handle watching him chase what she saw as an impossible dream and eventually left him—but Fuji kept working anyway.
His research caught Giovanni's attention, who offered to bankroll the entire project on one condition: clone Mew as well. That's how Mewtwo came to exist.
The cloning process was brutal. The starter Pokémon clones—Charmandertwo, Bulbasaurtwo, and Squirtletwo—all died during experimentation. Then Ambertwo, Fuji's cloned daughter, died too. The sight of it devastated Mewtwo, who was still developing emotionally at the time. Panicked, Fuji injected Mewtwo with some kind of emotion-suppressing serum to keep it calm. Whether that injection warped Mewtwo's personality later is anyone's guess, but the timing is suspicious.
After Mewtwo gained full consciousness, it didn't stick around. It destroyed the entire lab on New Island and apparently killed everyone inside—Fuji included.
Content compiled by AnimeList.moe from publicly available sources.