The flight instructor reported that the student pilot pushed the throttle about 3/4 of the way in during the takeoff roll, and did not add full power until about 1/2 way down the 1,500 foot grass airstrip. The airplane had not attained flying airspeed by the time it reached the end of the runway. The airplane became airborne, but it settled and impacted the terrain, which resulted in substantial damage to the fuselage and right wingtip. The flight instructor reported that there were no preaccident malfunctions or failures with the airplane that would have precluded normal operation.