How do you safely remove a swimmer with a possible head injury from the water?

Immobilization. If the swimmer has a head injury, assume he has a neck injury as well. The neck must be immobilized and the head kept in a neutral position (looking straight up when on the back). If you have a float floatation device (surfboard, boogie board) and a 2nd rescuer, place the board directly underneath the swimmer's head and upper back.
Very carefully!, Airway breathing circulation neck/spine stabilization while doing the other life saving maneuvers really all is done simultaneously and you need more than one person.