The flight instructor in the multi-engine airplane reported that during a biennial flight review the pilot released the brakes and added full power for takeoff. The flight instructor further reported that during the takeoff roll he utilized the left engine mixture control to simulate a left engine failure, but the pilot "froze" at the flight controls and the airplane veered to the left. The flight instructor attempted to fail the right engine via the right mixture control in order to regain directional control, but his hand came off the mixture control and the airplane exited the runway. During the runway excursion, the flight instructor "finally got [his] hand back on the right mixture and pulled it to idle cut-off"; subsequently, the nose landing gear collapsed. The airplane sustained substantial damage to the fuselage. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.