Players who wish to start a new game can start a new game by first deleting their current game. To delete their game, go to the game settings and tap on "Delete Account". Follow the prompts to confirm the account deletion. Once your account is deleted, you'll be able to start over with a new game.
If you wish to keep your current progress, but also want start a new game, you can first connect your existing game to a service like Facebook or Google. After successfully connecting to either service, you can disconnect either Facebook or Google. Once disconnected, your game will start from the beginning and your previous progress is saved to the account. However, if you want to save the new game progress, you will need to use another Facebook or Google account to connect to.