THE OWNER/STUDENT PLT & HIS INSTRUCTOR (CFI) WERE ON A DUAL INSTRUCTIONAL FLT & PROCEED TO AN ARPT WITH A WET GRASS RWY TO PRACTICE LANDINGS. THE RWY WAS 2200 FT LONG & HAD 50 TO 60 FT TREES AT THE APCH END THAT HAD BEEN CUT TO APRX 25 FT AGL. THE 1ST APCH (FOR A TOUCH-AND-GO LANDING) WAS HIGH, SO A GO-AROUND WAS MADE. THE 2ND APCH WAS BETTER, BUT THE STUDENT STILL TOUCHED DOWN APRX 1050 FT DOWN THE RWY. AT THAT POINT, THE CFI TOLD THE STUDENT TO MAKE A FULL STOP LANDING RATHER THAN A TOUCH-AND-GO. THE STUDENT APPLIED BRAKES, BUT FELT LITTLE REDUCTION IN GROUND SPEED. THE CFI THEN TOOK CONTROL & APPLIED HARD BRAKING. HE STARTED S-TURNS BUT COULD NOT STOP ON THE REMAINING RWY. EVENTUALLY, THE ACFT DEPARTED THE RWY IN A SKID, HIT A DITCH & THE RIGHT MAIN GEAR COLLAPSED. NO EVIDENCE OF A PREIMPACT MALFUNCTION OR FAILURE OF THE BRAKES WAS FOUND. ACCORDING TO THE ACFT HANDBOOK, 1650 FT WAS REQUIRED TO STOP ON DRY PAVEMENT WHEN LANDING OVER A 50 FT OBSTACLE.