Assuming this is X/Y ...
Before you take on Mewtwo, activate your Capture O-Power (hopefully L3 by now), and throw a Quick Ball right off. This gives you a fair chance for a first-turn capture.
After that, forget Ultra Balls, use Dusk Balls. He's in a cave, so Dusk Balls have a 3.5x catch rate, compared to 2x for an Ultra.