Cut out the area of termite-damaged drywall with a utility knife. Locate the studs for the drywall by tapping on the wall for the solid areas. Cut the drywall from the center of one stud to the center of the stud on the opposite side. Be sure the side studs are not termite damaged. If damage is apparent, cut to the next stud in the wall.
Measure the height of the damaged stud and cut a 2-by-4-inch board with a circular saw to fit. Align the new board flush on the side of the stud and nail in place with 4-inch nails. Place the nails at the top and bottom. Nail into non-damaged areas in the center.
Cut a new sheet of drywall to fit the opening. Screw the new sheet to the new piece of wood on the repaired stud using drywall screws. Drill screws into the two surrounding studs to hold in place. Apply drywall mud to the seams with a putty knife and allow to dry.