The flight instructor was providing initial flight training to the student. After completing hover and pattern work, they transitioned to a raised grass helicopter practice pad on the airport. After the student completed a successful set-down, the instructor asked him to lift the helicopter into a hover. As the helicopter lifted off the ground, it began to move aft, and the instructor applied forward cyclic. However, the helicopter continued, and he felt the right skid touch the ground. The helicopter then started to roll, and sensing that this could be the beginning of a dynamic rollover event, he reduced collective pitch control, however the helicopter yawed to the left and rolled over. The fuselage and tailboom were substantially damaged. The pilot reported that there were no mechanical failures or malfunctions with the helicopter that would have precluded normal operation.