DURING A TRAINING FLT, THE INSTRUCTOR (CFI) & STUDENT LANDED THE ACFT ON A ROUGH DIRT/GRASS STRIP THAT WAS 2200' LONG. THE CFI REPORTED THAT AS THE STUDENT WAS MAKING A ROUGH FIELD TAKEOFF FROM THE STRIP, THE ACFT BECAME AIRBORNE 'JUST BEFORE THE MIDDLE POINT OF THE RUNWAY' & 'AT THIS POINT, THE STALL WARNING BEGAN TO SOUND.' THE CFI SAID HE PUSHED THE YOKE FORWARD IN HOPES OF 'COAXING' SOME ACCELERATION, BUT THE ACFT'S SPEED REMAINED AT ABOUT 55 KTS & THE ACFT WOULD NOT ACCELERATE OR CLIMB. ACCORDING TO THE CFI, THE ACFT REMAINED ABOUT 10' ABOVE THE SURFACE & FELT OVERWEIGHT, UNDERPOWERED & SLUGGISH. THERE WAS INSUFFICIENT RWY REMAINING TO ABORT & THE CFI HOPED TO GET THE ACFT TO ACCELERATE, WHILE DSCNDG OVER A BLUFF BEYOND THE END OF THE RWY. HOWEVER, THE ACFT HIT A BUSH OR LOW TREE, THEN IT ROTATE ABOUT THE VERTICAL AXIS & CRASHED. THE CFI RPRTD THAT THE STALL WARNING CONTINUED TO SOUND UNTIL THE ACFT 'STARTED SLIDING DOWN THE BLUFF.' NO PREIMPACT MECHANICAL PROBLEM WAS FOUND.