At the successful completion of one practice straight-in autorotation to the grass area between the runway and taxiway, terminating with a power-on three foot hover, the CFI asked the student to repeat the same maneuver. On the second attempt, the student over controlled aft cyclic and caused a tail rotor strike before the CFI could recognize and counter the student's abrupt control input. The rotorcraft entered an uncontrolled right yaw until the landing skid caught the terrain, and rolled over on its right side. The student and CFI evacuated the rotorcraft out the left door, unhurt.