Mewtwo: the Pokémon that was built, not born

Made from Mew

In the original games, the story is told through journals left in the ruined Pokémon Mansion on Cinnabar Island. A scientist, Mr. Fuji, discovered the Mythical Pokémon Mew, took some of its DNA, and used it to create Mewtwo — a modified clone meant to be the most powerful Pokémon in existence (Bulbapedia).

It worked too well. After what the journals call horrific gene-splicing experiments, Mewtwo came out with extreme power and a vicious disposition. It broke free and destroyed the mansion on the way out. One journal even records its birthday: February 6 (Bulbapedia).

The Red and Blue Pokédex entry says it plainly: "It was created by a scientist after years of horrific gene splicing and DNA engineering experiments." Oddly, that line went untranslated in English at the time and only appeared in an English game when it was reused in FireRed (Bulbapedia).

The movie that made it a character

In the games Mewtwo is a monster waiting at the end of Cerulean Cave. The first film turned it into something more interesting.

Mewtwo Strikes Back opened in Japan on 18 July 1998 and in North America on 10 November 1999. In it, Team Rocket's Giovanni funds the project, and the scientists grow Mewtwo from a fossilized eyelash of Mew. Mewtwo is furious at being treated as the result of a project rather than a living thing, destroys the lab, rejects Giovanni, and sets out to prove that Pokémon and people cannot be friends (Bulbapedia).

That shift — from weapon to a creature asking why it exists — is a big part of why Mewtwo still has a grip on people who grew up with it.

On cardboard

Mewtwo's first English card is Base Set #10/102, a holo illustrated by Ken Sugimori. It was first printed in Japan in the original Expansion Pack and later reprinted in Base Set 2 as #10/130 (Bulbapedia). If you have one, check which set it is before anything else. The Base Set and Base Set 2 copies look very similar, but they are different cards from different sets.