To answer your question, feel free to visit the link here:

(http://www.freddiemac.com/uniform/unifsecurity.html#highlights

Once you are on the website above, scroll down and click on the "First Lien Security Instruments" for the State where your property is located in.  The information provided below is from the Rhode Island First Lien Security Instrument as this is the State where I live and is directly noted on Page 12 of 16 towards the bottom of the page:    

Transfer of the Property or a Beneficial Interest in Borrower.  As used in this Section 18, “Interest in the Property” means any legal or beneficial interest in the Property, including, but not limited to, those beneficial interests transferred in a bond for deed, contract for deed, installment sales contract or escrow agreement, the intent of which is the transfer of title by Borrower at a future date to a purchaser.

If all or any part of the Property or any Interest in the Property is sold or transferred (or if Borrower is not a natural person and a beneficial interest in Borrower is sold or transferred) without Lender’s prior written consent, Lender may require immediate payment in full of all sums secured by this Security Instrument.  However, this option shall not be exercised by Lender if such exercise is prohibited by Applicable Law.

If Lender exercises this option, Lender shall give Borrower notice of acceleration.  The notice shall provide a period of not less than 30 days from the date the notice is given in accordance with Section 15 within which Borrower must pay all sums secured by this Security Instrument.  If Borrower fails to pay these sums prior to the expiration of this period, Lender may invoke any remedies permitted by this Security Instrument without further notice or demand on Borrower.

Sure, pay the loan off.   

The simple fact is that paying the loan off is the only sure fire way to do it.  Banks, lenders, servicers will never, ever let someone off the loan if they don't have to.  The corollary of this is never, ever co-sign for someone, as it will always come to grief.

There is actually no way to have a co-borrower removed from a mortgage that I am aware of, if this is a traditional conforming or government guaranteed (FHA or VA) mortgage. 

When people get divorced, typically the judge will issue a decree stating that one of the two parties is responsible for the mortgage payment and the ownership of the home. This decree however does not remove the financial obligation of the transaction if there is a default.  All parties that signed the original note are still responisble. 

The only thing that can be done is to refinance the home without the other party. To do this it will be necessary for the other party to deed the property to you. Typically this is done by using a quit claim deed.. The title company being used for the refinance transaction can take care of this ownership transfer for you.