Is this a sign of an abusive relationship?

This does sound abusive. He should never grab you or try to damage your property. He has difficulty controlling his anger and communicating. He should not blame you for his behavior. Since you have been off and on he may feel you are drifting towards being off again but the issue is how he is treating you. Behaviors like this usually become worse with time. If you can't talk this through with him and he feels he has done nothing wrong, you need to move on.