I am assuming you restored the iPad from a backup and thus the reason you still have previous game data showing up. Anyway, do the following:
1. Delete the app and then reinstall it.
2. Go to Settings - iCloud - Storage - Manage Storage and then, under "Documents & Data, tap on "Show All".
3. If the game is listed, tap on it, then tap on Edit" in the upper right corner, and then tap on "Delete All". Afterwards, tap on "Done" in the upper right corner.
4. If the game has it's own cloud service that maintains the game's data then you will have to check the game's setting/options for a way to delete the data.