There are two options to turn off cloud storage for game saves:

Move saved games out of the cloud and turn off cloud saves First, you need to move your game saves out of the cloud. See Copy, move, or delete content for steps on how to move content from one storage device to another (for example, from Cloud Saved Games to Hard Drive).

Once you've done this, you can turn off cloud storage. Here’s how:

From the Xbox 360 Dashboard, go to settings, and then select System. Select Storage. Highlight Cloud Saved Games, and then press the Y button on your controller. Select Disable Cloud Saved Games. Keep saved games in the cloud and turn off cloud saves You can turn off cloud storage for a single console and keep your saved games in the cloud for you to use on another console. Here’s how:

From the Xbox Dashboard, go to settings, and then select System. Select Storage, and then select your primary storage device. Select System Items, and then select Cloud Storage Console Copy. Select Delete. Note You will be asked to confirm that you want your saved games to remain in the cloud, and future updates to your saved games will not be synced with this console.