You *can't* remove your name from the mortgage without--
1) Paying it off;
2) Someone else, like a co-owner, refinancing the mortgage solely in his or her own name; or
3) The consent, or agreement, of *all* parties to the mortgage, including the bank, to removing you---and the bank/lender will not consent, because it is not in their interest: removing you from the mortgage eliminates a person who is responsible to pay, and whom they could sue if they are not paid.
The mortgage is a contract: you cannot remove yourself from it aginst the will of the other parties to the contract, unless, as stated in 1) and 2) above, it is paid off or refinanced. So you need your co-owner to agree to refinance in his/her name alone, or you need the home to be sold and the proceeds used to pay the mortgage. If you want to sell the home, but the other owner does not, you can bring a legal action (lawsuit) for "partition"--that is, for a court order that the home be sold, the loan paid off, and the remaining proceeds (if any) distributed between the owners (after paying the costs of sale). This is the law's remedy for the situation where the owners can't agree on what to do with the property. If you want to explore this option, consult with a real estate attorney.
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