C172 Flight Instructor on training flight with student reported Taxiway Excursion during taxi out for takeoff.

Narrative

This safety concern is about a student attempting to assist on taxi resulting in the aircraft taxiing off of the taxiway into the grass. During the run-up; we conducted a brake check; and both brakes felt fine; but the left brake went down a bit further than the right brake leading to a slightly heavier right turn. We were given instructions to taxi via echo alpha to Runway XX. We turned onto taxiway echo and alpha perfectly fine; and while taxiing; I noticed my student beginning to taxi a bit faster than recommended. I told him to slow down since we were approaching the turn to Runway XX. He attempted to apply the brakes; and we started turning to the right. I told him to correct to the left; and he told me we had lost our brakes. I told him that I had the flight controls and attempted to correct with both brakes; followed by left brake and left rudder; but we continued to veer to the right; eventually stopping about 3 feet off of the taxiway in the grass. Nothing was damaged; and the aircraft was towed back to the ramp. I spoke with the student after the incident; and he told me that he was assisting me after I had told him I had flight controls because he froze up. We proceeded to have a lesson about the three point handoff method and how when I say I have the flight controls as an instructor that I need to be the only one touching the flight controls.