Examine the inside of the door. The handles of some early GE Spacemaker microwave models were attached after the two inner door panels were assembled to the outer door. If you see two recessed screws opposite the handle attaching points, undo them with a Phillips screwdriver and remove the handle. If not, go to the next step.
Insert the blade of a thin, flat-head screwdriver into the top, outer corner of the door, between the plastic inner frame and the outer door. Gently pry the inner frame out and slip a putty knife into the exposed opening on top of the door. Slide the putty knife toward the hinges to free the top of the inner frame; repeat on the front and bottom edges of the door and lift the inner frame out to expose a second metal inner frame.
Insert a thin, flat-head screwdriver into each of the small square openings on the top and bottom of the inner metal frame, starting at the handle end of the door. Undo the attaching clips by gently levering the inner door away, using the rim of the outer door as a fulcrum. Move the inner door away from the outer door on its hinges.
Remove the glass from the outer door. Undo the two screws holding the handle to the outer door with a Phillips screwdriver. Screw the replacement handle onto the door and tighten securely.
Replace the glass panel and reassemble the door by snapping the two inner frames back in place.