Shorts SD3-60 Captain reported loss of the normal braking system led to a taxiway excursion during taxi to take off. The flight crew secured the aircraft and awaited a tow crew to retrieve the aircraft.

Narrative

Aircraft preflight; start up; after start checks were normal to include brake checks from parked position and again as part of rolling taxi checks leaving ramp area. All systems appeared normal on the slow taxi to Runway XX. A med flight twin aircraft was ahead and begging to hold short of Runway XX as we began our turn left on Taxiway 1. Brakes were used sparingly with beta being the main source of speed reduction. There was a tailwind on taxi (340/11G23). Upon reaching the end of the run up area on our right side; I began to apply full beta and attempted soft braking to anticipate a full stop before our turn to hold short on Taxiway 2. After noticing no response I attempted a full application of brake with no avail. I let off and reapplied. With brakes failing to work; I vocalized BRAKES to FO (First Officer); went full reverse power on throttles; FO attempted to a full application of brakes. I simultaneously checked hydraulic panel for pressure indication for which we had none; let hand off throttles to ensure emergency brake was in the OFF position which it was in correct position. Left hand left the tiller momentarily to to verify the parking brake was off or stuck; returning to tiller. While we both were attempting brakes; I began a short turn toward Runway on Taxiway 2 in hopes the med flight aircraft would begin its take off; giving us room to stop. With the med flight still holding short; I turned our aircraft back to the left toward the grass in an opening. In full reverse and no brakes; the aircraft came to rest about 20 ft past the Taxiway 2. We ran shutdown checklist. FO notified ATC where we were and that we would need assistance but no emergency vehicles. Airport personal arrived at the plane while FO and I secured aircraft and made calls to Operations; Maintenance; Dispatch. Taxiway 2 was closed while we waiting for help to tow the aircraft. No damage was sustained to aircraft or airport surface. I think the brakes failed to work due to either a bubble in line; rigging/issue with emergency brake accumulator.