The flight instructor reported that during the instructional flight with the student pilot on the controls to practice a soft-field takeoff, the airplane started turning to the left "drastically" shortly after the airplane became airborne. The student told the flight instructor that he could not control the airplane, so the instructor assumed control to try and realign the airplane to runway centerline and re-touch down to abort the takeoff. Despite the flight instructors control inputs, the airplane continued to veer left and exited the left side of the runway. The airplane collided with the terrain substantially damaging the left wing.

The pilot reported no mechanical failures or malfunctions with the airplane that would have precluded normal operation.