You are confusing "owing" with "owning." Removing your name from the title (owning) does not relieve you of the responsibility for loans in your name that you promised to repay (owing). You can "owe" on property you do not "own." The divorce decree may have taken away your ownership to the property and given it to your ex-wife. Additionally you can deed your interest in the property to your exwife, but you are still responsible to the lender for the loan you took out until the loan is either paid off or the lender gives you a release.
So while you can quit your interest in the property you can't just quit your liability.
For you to be relieved of responsibility for the loan it must be paid off by your ex-wife refinancing or through the sale of the property. If the loan is assumable then your ex-wife can assume the loan and you can ask to be released of liability.
For specific legal advice please contact an attorney familiar with the laws in the state the property is located.