A Piper PA-44 Flight Instructor reported that while conducting engine failure on takeoff training; the student pilot hesitated executing the correct procedure. This caused the aircraft to veer off the paved runway surface; striking a light fixture and damaging a propeller blade.

Narrative

This was a Commercial Multi engine training flight; the incident occurred after practicing Commercial Airman Certification Standards (ACS) maneuvers and coming to a full stop at ZZZ after an instrument approach.After taxiing back to Runway XX; a practice engine failure during the takeoff roll was conducted. The instructor cut off the mixture of the right engine; anticipating the student to close both throttles and maintain directional control using rudder as previously trained according to the standard operating procedure of the flight school.After noticing the student panic; the instructor attempted to bring the aircraft under control by accomplishing the prescribed method of the flight schools Flight Operations Manual: 'If the student fails to immediately close both throttles; the instructor must quickly close the operating engine's mixture to cut off to maintain directional control of the aircraft. Then promptly close both throttles and advance both mixtures to full rich to prevent shutting down both engines on the runway.'The instructor closed the operating engine's mixture; but there was a delay between the closing off the mixture and the fuel supply to the engine being cut off; still allowing thrust on the operating engine momentarily. By the time the engine had shut down; the asymmetric thrust had already pulled the aircraft off of the runway environment. This caused the propeller of the plane to strike the REIL; damaging the light and propeller.The instructor was ready for the student to make the mistake of not acting; but given the time it took to react; and for the operative engine to fail by removal of the mixture; there was not enough time to overcome the asymmetric thrust with rudder and keep the plane on the runway.The aircraft came to rest in the grass; roughly 10 yards off the runway. No persons were injured; and the sole damages were to the REIL and the propeller of the right engine.