The flight instructor reported that he was on a cross-country training flight with a student. He said the student was performing an off airport landing where the elevation was 4,500 feet mean sea level (msl); the density altitude was reported to be 7,300 feet msl. The flight instructor said that as the helicopter approached the landing site, it began to yaw right, and the left pedal was ineffective. He took control of the aircraft, and noticed that the main rotor RPM was low. He lowered the collective slightly and rolled on additional throttle. The flight instructor said that the left pedal would still not turn the helicopter into the wind. He lowered the collective again, allowed the helicopter to settle, and then pulled collective to cushion the landing. The main rotor contacted the terrain and mesquite shrub. The aircraft came to rest on its left side, facing the direction from which it came, and the tail boom was separated from the fuselage.