C402 pilot reported a taxiway excursion due to brake failure.

Narrative

The previous leg from ZZZ occurred normally. After engines start; I was clear to taxi to Runway XX via Taxiway 1 and 2. I left the parking and joined Taxiway 1; the taxi speed was about 15kt. Before joined Taxiway 2; I applied the brakes and only the left brake worked. The plane veered to the left I was still on the taxiway. Then I released the brakes and tried to bring the plane back to the centerline; it did not work. At this point the left wheel was close to the edge of the taxiway. So; my reaction was to apply the brakes one more time but unfortunately; I skid off the taxiway to the left; all the wheels had contact with the grass. The plane stopped 90 degrees with the taxiway. I checked that there was no damage on the airplane and all the passengers were safe and without any injuries. I contact the Tower explained the situation; I didn't declare emergency and asked for a bus to deplane the passengers and also for a tug. A car from the airport operations came over to check out the situation. I called the ZZZ1 staff on the radio and explained the situation. Everything was under control at that point. The ground staff was very helpful and called a mechanic from a small company based in ZZZ1 to help me. All the passengers were deplaned on the taxiway and got on the bus. I helped the mechanic to tow the plane back to the parking. I did I walk around and we (me and the mechanic) found out some hydraulic leak coming from the right gear bay. I called Operations Control to explain the situation. I also called the on-Duty Manager.I wrote down on the can the discrepancy. Captain called me and we talked about the incident. At this point I was nervous but hopefully nobody got hurt. I called Operations Control again and explained that I was not fit to continue the journey. The guys were very understanding. Everyone that I talked were friendly and tried to help me.