How can I get my fiancée who cheated on me out of the house we bought together almost six years ago Both of our names are on the mortgage and the deed.

If the fiancee's name is on the deed, then they are a part owner and the ONLY way to get s/he out is a buy out. Being on the mortgage is really immaterial, but being on the deed means s/he has equal rights to the house. Since you aren't married you can't get a divorce and divide the assets as part of a divorce settlement.

You can mutually agree to sell the house and split the proceeds, but if you want to keep the house on your own, then you have to purchase the share from the ex.

P.S. It would help if you identified gender in posting. Makes it easier to respond. I had to go back and edit the gender specific parts of my response when I realized, your fiancée could be either male or female.