The flight instructor reported that he instructed his student to perform a soft-field takeoff. During the takeoff roll, the instructor had his hands on the flight controls while the student pilot released the yoke back pressure and the airplane began to climb, but the airplane's nose was too high. The flight instructor pushed forward on the control stick to correct the nose high attitude, "and the plane started to pull to the right." The flight instructor does not know whether the stall warning horn sounded, as the airplane flew over the right edge of the runway, but he does recall being on the flight controls when the airplane descended and impacted the grass safety area on the right side of the runway. The airplane sustained substantial damage to the lower fuselage composite structure. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.