After you have gotten all eight of your badges you need to go beat the pokemon league. The credits will roll and then the menu pops up again. DO NOT RESET THE GAME!!!! Go to Cerulean Citygo north to the brige where you faced 5 trainers before the path to Bill's house. Turn left and there will be a large area of water. Surf until you get to a cave. You will find Mewtwo in that cave.