PA44 INSTRUCTOR AND STUDENT AND PIPER ACFT HAD NMAC ON THE ILS RWY 32 AT CRG IN CLASS D AIRSPACE.

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WHILE ON AN IFR FLT PLAN; JAX APCH CTL CLRED US FOR THE ILS RWY 32 APCH CIRCLING TO RWY 14. AFTER THE HDOF TO CRAIG TWR; WE WERE INSTRUCTED (BY TWR) TO RPT 2 MI FINAL. MY STUDENT WAS UNDER THE HOOD AND I WAS WATCHING FOR OTHER TFC. WHEN WE WERE 6-7 MI OUT (ON FINAL) WE HEARD CRAIG TWR CLR ANOTHER ACFT IN THE PATTERN FOR A STOP-AND-GO ON RWY 14. I COULD SEE THE LNDG LIGHT FROM THE STOP-AND-GO TFC OFF IN THE DISTANCE. I WAS A LITTLE SURPRISED TWR CLRED THE PIPER FOR A TKOF IN OUR DIRECTION. UPON REACHING A 2 MI FINAL; WE RPTED OUR POS TO TWR. TWR THEN GAVE US OUR CIRCLING INSTRUCTIONS; 'TURN L TO ENTER A R DOWNWIND FOR RWY 14;' WHILE I REPEATED BACK. WE THEN CONTINUED ON DOWN THE GS ALL THE TIME WATCHING THE PIPER ON CLBOUT IN OUR DIRECTION. PRIOR TO REACHING OUR CIRCLING MINIMUMS; I HAD MY STUDENT REMOVE THE HOOD AND START A L TURN TO CIRCLE. I MADE SURE HE HAD THE PIPER IN SIGHT SINCE WE WERE ON A COURSE TO DSND BELOW IT. AS WE TURNED TO CIRCLE; THE PIPER PASSED OVERHEAD ABOUT 350 FT ABOVE US. THERE WAS NO EVASIVE ACTION TAKEN BY EITHER ACFT. HOWEVER; DURING THE DOWNWIND LEG; TWR ANGRILY ASKED US IF WE HAD UNDERSTOOD HIS INSTRUCTIONS. WE SAID WE DID AND REPEATED WHAT HE HAD TOLD US; 'TURN L AND ENTER A R DOWNWIND FOR RWY 14.' HE SAID HE HAD TOLD US TO 'TERMINATE THE APCH' WHICH NEITHER MYSELF NOR MY 2 STUDENTS ON BOARD HAD HEARD. I FEEL THE TWR SHOULD HAVE INFORMED US OF THE ONCOMING TFC OR NOT CLRED THE STOP-AND-GO PIPER UNTIL WE WERE CLR OF THE UPWIND. USUALLY TWR WILL RPT TFC DEPARTING AHEAD OF YOU WHEN ON FINAL -- ESPECIALLY IF THE TFC IS HDG TOWARD YOU!