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Tap the Settings app. Tap Accounts. Tap the account you want to turn off syncing for. Toggle Contacts OFF. Tap the button. Tap Sync now.

Article:
Unsyncing an account will remove all of the contacts that were synced from it. This can be useful for removing a lot of contacts at once. You'll find this in the Personal section. Any contacts from this account will be removed from your device. This will turn off contact syncing so that the contact list isn't automatically updated with your contacts from that account. If you don't see a Contacts option, toggle syncing off for that account completely. You'll see this in the upper-right corner. A small menu will appear. This will sync with the account, and since contacts were disabled all contacts for that account will be removed from your device.