Raise a Tyranitar and teach it Taunt. Whenever you use Taunt, Mewtwo won't be able to use Recover or Safeguard leaving him with two attacks left. Psychic, Mewtwo's strongest attack won't even do any damage to Tyranitar because Tyranitar is part Dark. Swift is a joke on Tyranitar because he is resistance to Normal attacks and Mewtwo's attack isn't as deadly as his Special Attack. Also, reteach Thunder Wave on Zapdos so you can have something to Paralyze it. You need to go to the Move Relearner in Island 2 to do that. Plus, you need either 2 Tinymushrooms or 1 big one. You can find mushrooms on wild Paras at Mt. Moon B1. They have a 100% encounter on that floor.
When you finally start the battle with Mewtwo, use Zapdos to Thunder Wave it. Zapdos is the fastest in your team so it needs to be the first Pokemon that you should use. When you successfully paralyzed it, switch to Tyranitar and a Sandstorm appears. Use Taunt on your next move and start throwing Ultra Balls after that. The Sandstorm will slowly damage it, making it a little easier to catch it.
Tyranitar takes awhile to get because he needs a lot of experience to level up but it is really worth it when it finally evolves into that form. I caught Mewtwo on my first try with a Level 55 Tyranitar.