Shortly after departure, the commercial pilot undergoing instruction leveled the helicopter for cruise at an altitude of 300 feet above ground level, in compliance with the flight school's departure procedures. He reached down to the instrument panel pedestal with the intention of pulling the cyclic right trim knob; however, the flight instructor observed him instead reach for the adjacent engine fuel mixture control. The instructor yelled for him to stop, and attempted to swat his hand clear, however, the pilot then pulled the control and the engine lost all power. The flight instructor initiated an autorotation while simultaneously pushing the mixture control back down. The engine did not restart, and the helicopter landed hard, with the main rotor blades severing the tailboom. The high density altitude conditions, along with the helicopter's altitude and airspeed at the time of power loss, meant that it was operating on the edge of the "Avoid Operation" area of the height-velocity performance envelope. The pilot reported no mechanical malfunctions or failures with the helicopter that would have precluded normal operation.