If both you and your fiancee signed a note and mortgage to purchase and refinance a home, you are both responsible for the payments. Until that mortgage is satisfied — paid off — that’s the way things will stay. So, unless one of you has a big pile of cash sitting around, the only way to accomplish that is either to refinance the mortgage or to sell the house.
My recommendation to you would be to come up with some ideas as to how you and your former fiancee plan to divvy things up and take your ideas to a lawyer to formalize your agreement. This is especially important if you are unable to sell the house or refinance it right away, since you will need a way to allocate expenses (mortgage, taxes, insurance, maintenance, etc) for the property while one of you remains in it and have a formula for divvying things up in the future.
A word on refinancing should you decide to go that route. Subject to maximum FHA loan limits for your county, FHA does not consider equity buy-outs to be a “cash-out” refinance. Thus, a person can borrow up to 97% of the value of their property to buy out a co-borrower. Get in touch with a knowledgeable broker or lender who does FHA loans to find out more.