Being married only a year, the house has both names on it, initially it was the husbands house and when they married the wife's name was put on, can he somehow void her name as he is paying the mortgage himself as she does not work. She receives funding from the government for a health issue which she spends on herself and her son. How can he prove that he pays the bills. Also, if she chooses not to work because she says "she gets more money without working than if she were to get a job"

Welcome to divorce the finding out it is often cheaper to keep them.

Because you put her on the deed there is no way to take her off unless the divorce court orders it. And they may see her as 1/2 owner and you may even end up paying her for her 1/2 of the equity in the house.

As for the mortgage, to get her name off, after her name is off the deed, you can refinance.

You didn't say whether the property was refinanced. Do you know? If she is not on the mortgage, then she can quitclaim her interest to him. He/she may need a lawyer.