A quitclaim deed transfers the grantor's interest in the property. A mortgage is not an interest in the property held by the grantor, it is a debt. Debts and financial obligations can not be transferred through a deed. That is one of the reasons mortgages are written such that the real estate serves as security for the loan but the loan proceeds are lent to the borrower as cash via a promissory note or other instrument. For all intents and purposes the borrower received cash, though the lender may have stipulated that the loan was made contingent on the proceeds being used to acquire the real estate used as collateral. So, the loan stays with the borrower and the real estate remains security regardless of whether the borrower relinquishes ownership rights.
Quitclaim deeds are one of the few methods of changing ownership of real property without triggering the "due on sale" clause of a mortgage, at least if the change in ownership interest is done for little or no consideration. In today's economy, some mortgages specifically list the relinquishing of all ownership interest, in any manner, as a default. Relinquishing all ownership interest would occur if you removed your name from the title via any type of deed but for the most part lenders are use to quitclaim deeds as they are used everyday to add or remove family members from property titles for various reasons.
There are ways to end your responsibility for an existing mortgage. See How to End Responsibility For a Mortgage.