Mewtwo was not included in the original release of Super Smash Bros. Brawl. He was added later as part of the "The Subspace Emissary" DLC, which was released as part of the "Super Smash Bros. Brawl: The Subspace Emissary" game disc.
However, to access this DLC, you need a specific version of the game.
* The original "Super Smash Bros. Brawl" disc doesn't include Mewtwo.
* You need the "Super Smash Bros. Brawl: The Subspace Emissary" disc, which is a separate release that includes the original game plus the DLC.
Even with the Subspace Emissary disc, you still need to complete certain conditions in the game to unlock Mewtwo. You must complete the Subspace Emissary story mode to unlock him.
So, while you can get Mewtwo in Super Smash Bros. Brawl, it's not as simple as just playing the game. You need the specific version of the game and need to complete the Subspace Emissary mode.