All of your Game Center data is stored in iCloud. This means that in order to delete your progress you must go to iCloud storage settings. It should only take a few minutes:
- Go to Settings > Apple ID Profile > iCloud
- Tap Manage Storage
- Look for the game you want to restart and tap it
- Select Delete Data – remember this action deletes all data for this game from all Apple ID connected devices
- A message pops-up asking you to confirm the deletion