The flight instructor reported that, during takeoff, as the airplane reached rotation speed, the student took his feet off the rudder pedals. The airplane drifted left of the runway centerline, and the student then quickly placed his feet back on the pedals and pushed the right brake, which caused the airplane to veer right. The instructor, who did not have brakes on his side, applied left rudder, but the airplane departed the right side of the runway. He added that, during the runway excursion, he heard the tail dragging along the ground or striking bushes. Subsequently, the airplane aligned with the runway, but fearing damage to the tail, the instructor aborted the takeoff and landed the airplane on the side of the runway, and it struck large mounds of dirt and a ditch. The airplane sustained substantial damage to both wings and the fuselage. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.