Your mortgage was a contract between you and your then spouse and the bank. Mortgages -- or vehicle loans, or lease agreements, or other contracts for that matter -- do not come with a "If we break up we get to choose who stays in the contract" clause. The marriage may have severed the contract that you and your spouse formed when you signed the marriage contract, but it does not sever any other contracts you two signed jointly.
Contact your divorce attorney's office. The first thing you will be told to do is complete a quit-claim deed. Your divorce attorney's paralegal will spend 30 minutes putting one together. It will cost very little to accomplish part 1. The second thing you need to do is a bit more difficult -- you need to refinance the mortgage. The difficulty of refinancing depends on the amount of equity the homeowner has in the property, the homeowner's employment status, credit score, and debt-to-income ratio.
You mentioned it will cost you $14,000 in closing costs to refinance the mortgage. That seems steep to me given the facts presented and I am curious as to why you are being asked to pay 8% of the value of the mortgage to refinance it. My second reaction is to recommend that you shop around. For no-cost refinance quotes from up to four pre-screened lenders, visit the Bills.com refinance savings center.
I hope this information helps you Find. Learn & Save.