If you want to remove a cosigner on the loan, you will need to pay the loan off. This can be done by paying it off or refinancing in your name only. The lender will not just remove a name.
If you want to remove a co owner on the deed, all parties need to agree and a lawyer can redo the deed for a few bucks.
I assume you mean from your mortgage and title. And as src50 said, there is no such thing as a co-signer on a mortgage. They are actually a co-owner. Since the other person is a co-owner, the only way you remove them is to buy them out - usually by refinancing the mortgage under your name only. If you do not qualify for a mortgage on your own, you are pretty much stuck.
If that name is on your deed then they are much more than a co signer- they would be a co owner. You would need to come to an agreement and "buy" them out. If they will agree to it for $10.00 then that would be fine but they must agree to it. If they are not on the deen but just on the note then you just need to refinance your loan.
Deeds don't have cosigners. Loans do. If you mean a joint owner, you can't remove him/her without consent.
