The pilot reported that the left brake failed to function during taxi when he attempted to reduce speed and turn 180 degrees into the takeoff position. The airplane began to track to the right. He released brake pressure on both pedals thinking that he might have been applying pressure to the rudder pedal instead of the brake pedal. He then reapplied pressure and experienced the same results. At that point, he reduced the power to idle. The airplane ran off the side of the runway, traveled down an embankment, and flipped over. Examination of the aircraft revealed a hole in the left brake-system pressure line behind the co-pilot brake pedals. The hole had resulted from chafing between a mounting clamp and the line. The line and clamp were properly installed. The hole was not visible until the clamp was removed. Corrosion was also noted on the line in the area of the hole. A search of FAA SDRs revealed no reports of similar failures.