The flight instructor and pilot receiving instruction reported that, the pilot performed a soft field takeoff and once in ground effect, he reduced back pressure and the instructor heard the stall warning horn and observed a low airspeed. The instructor told the pilot to reduce the pitch, the pilot lowered the nose a little, but the airplane continued to climb. The instructor told the pilot to reduce pitch again, but the pilot reported he was concerned about a possible propeller strike. The flight instructor took the flight controls, but the airplane had turned to the right and he experienced a "loss of control". The airplane landed off the right side of the runway, the instructor reduced power, the left main landing gear separated, and the airplane came to rest. The instructor and student reported that the airplane had aerodynamically stalled. The airplane sustained substantial damage to the fuselage. The flight instructor and pilot receiving instruction both reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.