Part 36: Omni's Asides - MewtwoRegarding Mewtwo in Pokemon Special/Adventure.
Mewtwo was the result of Blaines work at gene-modding Pokemon when working for Team Rocket, from the moment Red met him he was operating on borrowed time, as he had lent some of his own cells to the process of helping Mewtwo grow quickly (this is also the reason given why Mewtwo is more humanoid than Mew is) Unfortunately this backfired on Blaine, pretty horribly in fact.
The "My body was now symbiotically linked with the insane genetics experiment that is slowly eating away at my body and going to kill me if I don't find a cure and I can't find a cure without Mewtwo." kind of horrible. Mewtwo's motivation is, mostly, to be left the fuck alone and to tear shit up. Unlike in the Anime where it had a clear desire for revenge and a sense of purpose, Mewtwo in the manga is more... a wild pokemon before its capture and a fully realized being after its capture. His capture was orchestrated by Blaine and Red... well by Blaine at least, Red just stumbled upon the scene. Much like any sane child, Mewtwo was captured by Red using the Master Ball since Mewtwo responded to any singular challenge with Psychic Spoons and multiple pokemon with a psychic whirlwind.
Red would basically sling shot himself into the eye of the whirlwind before throwing his Pikachu, who threw the masterball to catch Mewtwo.
Mewtwo himself is mostly cool working with Blaine through the Yellow and GSC arcs, but eventually goes off on his own once their genetic link stops being a requirement. He does return in the Fire Red/Leaf Green arc however, for a multitude of reasons. Most notably to 1. Cut the Battle Tower in half like this was Revengeance
And 2. To face down a Giovanni lead Deoxys by Reds side