Can I purchase my son's cottage using a quick claim deed if I need to get a mortgage and he has a mortgage to pay off?

First of all, you are referring to what is known as a "Quit Claim Deed," not a quick claim deed. Unfortunately, if you need a mortgage, your mortgage company will dictate a lot about what you will have to do. They probably will not want just a quit claim deed, but the form of deed is not really very important. Check with your mortgage lender. Good luck.