How to Unsync Google From an Android Device
By default, Android 4 and Android 5 phones and tablets sync information from many of Google's services, including Google Calendar, Gmail, Chrome bookmarks, Picasa Web albums and Google Play Music uploads. To stop Android from syncing any or all of this information, deselect the Google components you don't want updated in the Settings app. If you want to stop not only Google but all accounts from syncing, turn off automatic synchronization.
Un-Sync Google Components
Open the Settings app or menu on your device and tap "Google" in the Accounts list. Some devices display accounts inside the Personal section of the Settings.
Select the Google account you want to stop syncing.
Uncheck the box by each Google service you want to un-sync. To completely stop Google from syncing any information, uncheck every box in the list. If you need to stop syncing multiple accounts, tap "Google" to back out and pick another account. When you finish, press the "Home" button to close the Settings app.
Stop All Automatic Synchronization
Run the Settings app on your Android and tap "Data Usage."
Open the menu by tapping the "Menu" icon in the corner of the screen -- or pressing the "Menu" button on some devices -- and uncheck "Auto-Sync Data."
Press "OK" on the warning to acknowledge that your Android won't keep any of your accounts synced or display notifications for updates.
Select an account from the Accounts list in the Settings app, open the menu and press "Sync Now" to sync an account manually. With auto-sync off, you need to perform this step for each account separately every time you want to sync.