Air taxi pilot reported brake failure during taxi resulted in a temporary loss of control and taxiway excursion.

Narrative

I was acting as a PIC on Aircraft X on a FAR 135 VFR flight from ZZZ - ZZZ1 with 9 passengers onboard. On preflight and taxi out checks the aircraft showed no issues. Upon approaching the end of Taxiway 1 at Runway XX Holding point; I contacted Tower advising we were ready for departure. Suddenly my aircraft lost right brake pressure and started steering to the left rapidly. I doubled checked engines and they were fully idle. I applied right brake pressure and right rudder but no input seemed to take effect on the motion already happening. At 45 degrees into the uncommanded and uncontrolled left turn both mixture levers were set to cutoff; as more brake pressure was applied with no effect. The aircraft came to total rest at a 90 degrees from taxiway center line; parallel to Runway XX hold short signs and pavement mark; with the nose gear wheel appropriately 1 foot inside the grass. Communicated tower on the issue; I set parking brake. Checked on my passengers and everyone was ok. Came off the aircraft and checked its surroundings; made sure the aircraft didn't impact any taxiway edge lights pole. No signs of damages to aircraft and or airport property were noted. Aircraft was deplaned and passengers taken to the FBO via ground transportation. FBO Maintenance team arrived at site pushed aircraft back into the taxiway and towed to the hanger were maintenance was performed. After performed inspections of the brake and steering system; both brakes were bled and master cylinders were serviced and aircraft was returned to service.