You can catch Mewtwo easily by using a Master Ball on it or by using an Ultra Ball on it after lowering its HP.
since you're in a cave,i could recommend a dusk ball.
I prefer to use my Master Ball for Mewtwo, but at least use an Ultra Ball.
You can probaly catch him with a ultra ball but I would use the master ball
With a master ball.
Throw a Master Ball at it.
master ball ultra ball quick ball or a premier ball
Well it matters what game you have, if you have Pokemon fire red, you can catch it with a master ball
to catch suicune,mewtwo,raikou and entei
The only sure way to instantly catch any Pokemon is with a Master Ball.
You could if you were to damage Mewtwo or cause status problems to him... I recommend a Ultra Ball.