With today's rules, you use some legal document to transfer the property ownership to him. After you sign, you are no long own that property.
Buy if the mortgage on the property was borrowerd by you or both you and your ex-hu*****and, you can not remore your name or liability from that mortgage note.
I have seen many cases one side own th house without refi and later ruin another side credit.
The only way is to do a refi to pay off the mortgage you borrowed.