It is totally unstoppable, usually goes on killing sprees.
It tries to kill pikachu in a movie, but fails
It hides in a cave near Cerulean City and kills anyone who enters, unless you have a master ball.
The master ball is your only means of survival against this monster
Person 2: "How did u survive? Come you weren't killed like everyone else?"
Person 1: "I had a master ball!"
"This is embarassing but he was beaten by a Porygon.. But his trainer sucked, so yeah."
"Mewtwo... I, Sephiroth, shall destroy you-- Cloud! I know your secret damn it!"
In "Mewtwo Strikes Back",it created an army consisting of all 3 Kanto starters,Ninetales,Vaporeon,and many others.Theese clones were stronger than the originals and nearly killed them all.But after a mushy moment,all the clones (including Mewtwo) left.In "Return of Mewtwo",Giovanni tries to re-capture Mewtwo but eventually falls to Mewtwo's awesome power.
In the games,it is only catchable in FireRed & LeafGreen.After defeating the Elite Four,you can return to Cerulean City,find the cave,and catch a Lv. 70 Mewtwo.It is the only Pokemon in FR & LG that sits at Lv. 70.
-Mewtwo,Pokemon Pearl Dex entry