Only hydraulic power can move the stabiliser on the 777. If the switches are in CUTOUT, hydraulics are removed from the hydraulic motors in the tail. The Cutout switches close hydraulic shutoff valves electromechanically.
During alternate control, mechanical linkages (between the flight deck and the tail) operate "arm" and "control" hydraulic valves on the STCMs, but if CUTOUT is activated, no hydraulic pressure reaches these arm and control valves.