When catching Mewtwo you need patience.
First hit him with stat lowering moves, than begin to highten your defenses.
Than try and hit him with hypnosis, so that you can weaken him without recover.
Than of course when he wkes up, he'll use recover, but thats why you need to lower his stats, so recover doesnt work as much.
Once hes back in the red, use hypnosis again, than throw ultra balls, if that doesn't work, prolong the battle as long as possible and use timer balls.
Works for me everytime. No matter what team im using.