Ok aside from the what is stated in the video games, if I remember correctly, Mew was more of a myth and thought to be at the very most extinct. Dr. Fugi, who had already been working on cloning, went in search for any remains of mewMew. After having found what he thought to be fossilized Mew remains he began to clone it for the leader of team rocket GiovanniTeam Rocket, Giovanni (having to tweak the DNA a bit). The name Mewtwo comes from the way Dr. Fugi named all his clones (bulbasaurtwoBulbasaurtwo, charmandertwoCharmandertwo, etc) although Mewtwo beingwas the only one twoto survive. It was only after Mewtwo escaped that the original mewMew was discovered to not be extinct.
Editor's note: I had to do some digging to get something more solid than my own and similar vague souvenir. I know the answer is a bit old but I figured I'd share my findings since the comment inquiries for sources.
The information above comes from comes from the first 2-3 minutes of the 10-minutes long short Myutsuu To Ai / Mewtwo / Mewtwo and Amber (Ai in Japanese) (Ai in Japanese), more commonly known in English as The Birth of Mewtwo, which was shown on the Japanese television the first time Mewtwo Strikes Back aired.
The whole short (specifically the last 7 minutes) was rated PG-13 due to the somewhat troubling/controversial topic(s) for children and thus, 4Kids Entertainment decided not to include more than the G-rated first 3 minutes intro (under the title Mewtwo's Origin) in the theaters and DVD releases of Pokémon: The First Movie - Mewtwo Strikes Back, which was enough to grossly explain to the Western public about the origins of Mewtwo.
The full ten-minute short is now available in the DVD release of Pokémon: Mewtwo Returns.
The entire short's transcript is available at multiple locations online, the specific website that sent me on the right track was: http://www.lchr.org/a/23/et/amberkins.html