Our game is designed so that players cannot easily lose their progress, and thus, the progress is saved on the server.
Currently, there is no option to start a new game as there is no Game Over in the game. You can always get coins and continue playing. Meow-the-way, if you use any other device, you can download the game there and start a new.
This option may appear in the future, and we surely will notify you if that happens! Despite that, try to take the next challenge and complete the levels.