Check with an accountant and a lawyer. I am neither, so what I'm mentioning here shouldn't be construed as either legal or accounting advice.
I'm guessing that you want your name put on the mortgage in order to take the tax deduction? If so, there are a number of ways that can be accomplished. (One, for instance, is by having your parents create a land trust--call it the Weidner Family Land Trust, though the name doesn't matter. Move the property into the trust. Then have your parents grant you a beneficial interest in the land trust. A beneficiary of a land trust is entitled to take the same deductions as the owner/former owner in this case is entitled to.)
One comment below says that your father wouldn't be able to act without your mother's cooperation. That really depends on whether she had a living trust, or has granted him a power of attorney. Again, I'm not a lawyer, but there are circumstances in which your father could legally act on your mother's behalf.
It's not too likely that he'd be able to remove your mother's name from the mortgage. Lenders like more security, not less. And, regardless of the circumstances, they don't like to remove names. A way around that would be for your father/parents to refinance the property in his name alone, if the lender is agreeable. Or, to refinance the property, with your and his names on the mortgage. But, as the others say, I'm not sure why you'd want to do that.
There probably would also be a variety of tax implications...especially if you start doing things with ownership/the deed.
So, check with a lawyer--an estate lawyer--and an accountant.
Hope that helps.