PA-34 Flight Instructor reported while taxiing the left brake failed resulting in loss of aircraft control and a taxiway excursion.

Narrative

While conducting a dual training flight in a PA-34 the student and I each conducted a brake check when exiting the ramp parking space. I noticed that the left brake felt slightly softer than the right. We were instructed to taxi via Taxiway 1 and Taxiway 2 to runway XX. When turning onto Taxiway 2 the student noticed that the left brake was increasingly ineffective. When given instructions to yield to a Citation approaching Taxiway 2 via Taxiway 3 the left brake failed completely; and the application of the right brake turned the aircraft to the right. The nosewheel of the aircraft exited the taxiway onto the infield by about 1-2 feet before we were able to come to a stop. I radioed Ground Control about our situation. We were able to use asymmetric thrust from the right engine to get the aircraft safely back on the taxiway centerline. Once there we requested and received taxi instructions back to the ramp via Taxiway 3 and Taxiway 4. Using asymmetric thrust and nosewheel steering we were able to return to the ramp without further incident.