The flight instructor reported that while conducting a simulated engine failure, the student terminated the maneuver, with the fuel mixture leaned, by advancing the throttle. The engine did not respond with full power, and the flight instructor then “advanced” the mixture. The engine subsequently lost total power. The flight instructor attempted but could not restart the engine. The flight instructor then selected an off-airport landing site, and during the landing roll, the airplane impacted a dirt “berm” which resulted in substantial damage to the fuselage. Postaccident examination of the airplane by the flight instructor revealed the mixture was not in the full rich position and the fuel pump switch was not in the on position, which was contrary to the checklist for engine failure after takeoff procedures. According to the owner, who conducted a postaccident engine test run, the engine exhibited no mechanical malfunctions or anomalies that would have precluded normal operations.