You can definitely capture Mewtwo with Pokeballs. The capture rate is a lot lower than common field Pokemon, but it's definitely possible. Weaken Mewtwo, put a status effect on it, then proceed to toss Pokeballs or whatever balls you want.
You can catch Mewtwo easily by using a Master Ball on it or by using an Ultra Ball on it after lowering its HP.
I prefer to use my Master Ball for Mewtwo, but at least use an Ultra Ball.
Master Ball
You can probaly catch him with a ultra ball but I would use the master ball
master ball ultra ball quick ball or a premier ball
With a master ball.
Throw a Master Ball at it.
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.
Try to get a ultra ball
a master ball preferably but any ball will work with a bit of luck