My Girl friend needs a surgery she can't affored can the hospatail turn her away because she can't afford even though she can't afford it??

It will depend on the hospital, in the US most areas have state funded hospitals, as long as it is a required surgary, they will have to take her.

Private hospitals can turn you away if you can not afford

Have her go to a county hospital and see if they can help her. It all depends on what kind of surgery she needs as you didn't say. If it is life threatening then the county hospital will have to do it.