The GameShark cheat code to catch Mewtwo in "Pokémon Emerald" for the Game Boy Advance SP is 25214170, according to IGN Entertainment Games. After entering the code, walk through any tall grass in the game until you encounter Mewtwo. This happens quickly, as the GameShark code disables other Pokémon.
Make the battle against Mewtwo much easier by walking through grass in lower level areas of the game, such as route 101 or route 103. GameShark automatically adjusts the level of any Pokémon code entered to correspond with the level of Pokémon in the area, allowing you to catch Mewtwo using your low level starter Pokémon at the beginning of the game.