The pilot reported that during a simulated engine failure after decision speed (V1) takeoff, when the flight instructor reduced power on the airplane’s left engine during the takeoff roll, the airplane yawed left and veered toward the left edge of the runway where there was packed snow. The pilot reported that he applied right rudder and back pressure to rotate the airplane as the instructor pilot added right rudder with his set of rudder pedals. The instructor pilot reported he then attempted to restore left engine power as the airplane struck a snowbank on the edge of the runway. The airplane exited the left side of the runway and came to a stop. The airplane sustained substantial damage to the engine nacelles and the fuselage. The left engine was separated from the airplane and the right engine remained attached by skin. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The instructor pilot reported that the flight’s purpose was for the pilot to conduct training in a twin-engine turboprop airplane, in preparation of an upcoming checkride. The plan was to simulate an engine failure during the takeoff roll, after passing takeoff decision speed (V1). He added that the plan was briefed the day prior and that the speeds were calculated and confirmed in the primary flight display (PFD) before the takeoff. The instructor pilot added that the runway was plowed 75 ft wide, with patches of packed snow near the edges.