If my separated husband signs a quit claim deed does that release him from responsibility from the mortgage also?

No, you will have to refinance and get the mortgage out of his name.
Even after her signs the quitclaim deed, the lender will still hold him liable since he is on the mortgage.

He must get off the mortgage or he will be held responsible financially.

If my separated husband signs a quit claim deed does that release him from responsibility from the mortgage also?
Short answer is no: Quit-Claim deed is a legal document w/the County. A mortgage is a legal document/agreement w/the bank.