MISCOM WITH GND CREW LANGUAGE BARRIER. TAXIED OVER TOWBAR; DAMAGED ACFT.

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DURING PUSHBACK OF FLT FROM SAIPAN TO GUAM; WE WERE TOLD TO SET OUR BRAKES BY THE PUSHBACK CREW AFTER WE HAD BEEN PUSHED INTO A TAXI POS. WE THEN PROCEEDED TO START ALL ENGS. WHEN THAT WAS DONE; WE EXPECTED TO BE TOWED FURTHER AS THE GATE AGENT INDICATED THEY PUSH US TO A SPOT FOR OUR START TO MINIMIZE THE EFFECTS OF THE WIND DURING START THEN TO ANOTHER LOCATION. SOMETHING UNINTELLIGIBLE WAS SAID BY THE GND HANDLER AND THE CAPT ASKED 'DO YOU WANT THE BRAKES OFF?' EXPECTING HIM TO TOW US FURTHER. HE REPLIED SOMETHING TO THE EFFECT OF 'AFFIRMATIVE;' SO WE RELEASED THE BRAKES; FELT THE AIRPLANE GOING FORWARD -- BUT ASSUMED IT WAS BEING TOWED (IT WAS NOT). CRUNCHING SOUNDS FOLLOWED AND THE BRAKES WERE SET. THE TOW BAR (DISCONNECTED FROM THE PLANE) HAD BEEN RUN OVER AND PUNCTURED 1 NOSEWHEEL TIRE. FORTUNATELY NO ONE WAS HURT! OBVIOUSLY PROB WAS WITH A LACK OF CLR COM; ALSO THE PUSHBACK DRIVER'S DIALECT WAS HARD TO UNDERSTAND. IN ADDITION; OUR ANTICIPATION OF FURTHER TOWING SET US UP TO EXPECT A BRAKE RELEASE AND FURTHER TOW SOON AFTER ENG START.