DA-42 Flight Instructor reported that while training an aborted takeoff during departure the student didn't follow proper procedure; resulting in loss of directional control and a runway excursion.

Narrative

On the return cross country from ZZZ1 we were completing pattern to finish the lesson at ZZZ. Prior to departure Flight Instructor briefed student on aborted take-off procedures and how we were going to demonstrate the aborted take-off on the ground prior to rotation. The explanation was as follows: Once you increase power to full raise your right hand above the throttles and I will take one of your engines out; after that you will take out the opposite and maintain centerline. Flight instructor asked student pilot if they had any questions prior and there were no questions asked prior to demonstration. After clearance for take-off and entering the runway applicant added in full throttle and held their hand briefly against the throttles before raising it above as instructed. Flight Instructor pulled left engine power to initiate the aborted take-off. Student then failed to take out the power immediately and instead attempted using rudders & brakes to maintain centerline; but aircraft then aimed off of the runway. Flight instructor took controls; removing right engine power and adding in significant brakes in order to slow down as we entered the rocks/gravel to the left of runway XX L. No damage was done to either aircraft or runway environment. Airport operations were required to tow aircraft out of the gravel and back to the hangar.