A PA28 INSTRUCTOR PLT RPTS A RWY EXCURSION AFTER TAKING CTL AS THE ACFT YAWED BECAUSE OF A STUDENT'S INCORRECT RUDDER INPUT DURING A XWIND LNDG.

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THIS OCCURRENCE HAPPENED WHEN LNDG ON RWY 23 THE STUDENT WAS FLYING THE PLANE AND I (THE INSTRUCTOR) WAS FOLLOWING ALONG WITH THE CTLS. THERE WAS A L XWIND CONDITION. THE EXACT VELOCITY IS UNKNOWN; BUT IS GUESSED TO BE AROUND 10 KTS WITH GUSTING PROBABLY TO 15 KTS. ON SHORT APCH I HELPED THE STUDENT PUT IN THE PROPER XWIND CORRECTIONS. UPON REACHING GND EFFECT; I HELPED THE STUDENT LAND THE AIRPLANE. UPON LNDG; I SUSPECT THE STUDENT PRESSED ON THE L RUDDER TO STRAIGHTEN THE PLANE OUT; BUT PRESSED THE RUDDER WITH TOO MUCH FORCE. THIS CAUSED THE PLANE TO YAW TOO MUCH TO THE L AND THE PLANE WAS IN A SIDE-LOADED CONDITION. THE R WING DIPPED TOWARDS THE RWY AND THE L MAIN WHEEL CAME OFF THE GND. I IMMEDIATELY TOOK OVER THE CTLS AND GOT ALL WHEELS BACK ON THE GND. THE AIRPLANE AT THIS POINT WAS FACING APPROX 45 DEGS TO THE L OF RWY HDG. INSTEAD OF TRYING TO AGGRESSIVELY STEER THE PLANE BACK ONTO RWY HDG; I FELT IT WAS SAFER TO CONTINUE GOING STRAIGHT INTO THE DIRT OFF THE L SIDE OF THE RWY. I CONTINUED UNTIL REACHING THE TXWY RUNNING PARALLEL TO THE RWY. I THEN PARKED THE PLANE; SHUT IT DOWN; AND DID A VISUAL INSPECTION FOR ANY DAMAGE. NO DAMAGE WAS FOUND AND THE PLANE WAS THEN STARTED BACK UP AND FLOWN TO MY HOME ARPT.