Here are some tips:
1: Get his HP into the red.
You already knew this, but keep in mind that Mewtwo knows Recover. False Swipe is the best move to get his HP to the lowest possible point.
2: Give him a status effect.
Pokémon with a major status condition are easier to catch. I suggest paralyzing it with Thunder Wave. Paralysis is the best because Sleep isn't permanent, and Burn and Poison might KO him.
3: The right Poké Balls.
Ultra Balls and Dusk Balls will have the highest catch rate. You can also throw a Quick Ball on the first turn and hope for the best, or pile up on Timer Balls — after 10 turns have passed their catch rate goes up.
4: Bring healing items.
Mewtwo is one tough cookie so pile up on Max Revives and Hyper Potions.
5: Save before attampting capture.
This way, if you accidentally KO Mewtwo you can just reload your save and try again.
6: Pick the right Pokémon.
Assuming this is in XY, I suggest Aegislash. It's bulky enough to tank Psychic in Shield form, is immune to Aura Sphere, and learns False Swipe. Make sure it knows King's Shield to get back in Shield Form, Swords Dance because Mewtwo likes to raise its defense with Barrier, and of course False Swipe. Maybe Shadow Sneak as well to knock off chunks of HP early on.