How do you take a person off the mortgage without refinancing?

This is normally not possible. If two or more parties signed a promissory note and a mortgage they are signing a contract that they obliging themselves to make good on that contract. Like any other contract, in order to get out of it, you have to convince the other party to release that obligation. This normally entails giving them some consideration. This consideration is normally the money that was lent out. Having said this everything in life is negotiable so you might be able to negotiate a release for a lesser amount or for different consideration.