How do you catch a Mewtwo with Great Balls?
I caught Mewtwo with a Pokeball, so listen closely. Mewtwo is Level 70 after you defeat the Elite Four and establish connection with Pokemon Sapphire and Ruby. Be sure to capture any Pokemon with Thunder Wave. Set it first. When you battle Mewtwo, use Thunder Wave (Mewtwo is probably going to use Safeguard). Then, have a fairly strong Pokemon (Level 64-66) and weaken it all the way until your next move will make Mewtwo faint. Mewtwo should not have a lot of moves used because it is paralyzed. Switch to an EXTREMELY weak Pokemon (Level 10-30) that is not super effective against Mewtwo. Keep on using weak moves such as Tackle, Pound, etc. until Mewtwo’s HP has very little left (so that you can barely see the red). Then, use Great Balls, Pokeballs, Ultra Balls, etc.