You can cancel your Liberty Mutual car insurance, but you will be charged for early cancelation. The cancelation fees and refunds depend on your state, so you should speak with your local agent to get the complete information. Keep in mind that gaps in car insurance will cause your premium to go up, so buy another car insurance before canceling your current one. During our Liberty Mutual reviews, we’ve found that many of the complaints were about increased prices due to the insurance gaps.