How can i delete all game data from my game center

Since the release of iOS 10, all of your Game Center data is now stored in iCloud.

To remove all of your game's data, try the following:

1. Tap on Settings > Apple ID Profile > iCloud
2. Tap on Manage Storage.
3. Look for the game in the list of apps that iCloud backs up data for and tap it.
4. Select Delete Data. Note: This will delete all data for this game from all Apple ID connected devices.

Try the following to delete a game and all of its related data:

1. Tap and hold on the game you wish to delete.
2. When the icon begins to wiggle, tap the X in its upper left corner.
3. Tap the X.
4. Press Delete.
5. Repeat the above steps for each game you want to delete.

Ref: Everything you need to know about Game Center - iMore