Yes, but Mewtwo is Powerful and very hard to capture even with an Ultra Ball. Best way to do this is Paralyze it, and bring it down to the red HP level.
Moves: Safeguard, Recover, Psychic & Swift
Level: 70
Location: Cerulean Cave
I suggest you take 99 Pokeballs and some high leveled Pokemon as Mewtwo is not all fun and games as its very Powerful, fast and has Fair Bulk. Be prepared and Good Luck.
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The only legitimate way to obtain Celebi and Mew is through a Nintendo event. In FireRed and LeafGreen you will need an event-only item to travel to the last two islands where you can catch those Pokemon
I don't think you can catch MEW without a action replay. But you can catch MEW2 in Pokemon Fire Red or Leaf Green. You CAN'T cach mew without an action replay, but you can trade mew-two from the other games to the newer ones
Mt.Moon
You can only using a Nintendo mystery gift.
mew-two is lvl. 70 in cerulian cave. make sure you save a masterball for him