The certified flight instructor said he and his student were flying the helicopter in the traffic pattern on the downwind leg. The student pilot was flying and he was told by the instructor to reduce the power to begin the descent for the base turn to final. The student reduced the power by approximately 1 inch of manifold pressure. The instructor then took control of the helicopter and reduced the power by an additional 6 or 7 inches of manifold pressure. He said that the student pulled the mixture control out to the idle cutoff position, which resulted in a loss of engine power. The student had intended to apply carburetor heat and instead inadvertently moved the mixture control, which was located next to the carburetor heat. The instructor turned the helicopter 180 degrees into the wind and simultaneously entered an autorotation from 300 feet above the ground. His selected landing site turned out to be a school yard with children present. He maneuvered the helicopter to a new landing site, but subsequently landed hard. The landing skids were spread and the main rotor cut off the tail boom.