SR20 Flight instructor reported their student pilot lost brake pressure during landing resulting in momentary loss of aircraft control and runway excursion.

Narrative

Student solo xc from ZZZ1 to ZZZ on Day 0 using pilotage and dead reckoning as trained. Preflight of the airplane was great and on the approach into ZZZ student checked brake pressure as prescribed in the cirrus checklist and had full brake pressure. When student landed on the ground in ZZZ it was a planned full stop taxi back to the runway and was slowing down using braking. As the student was making a right turn off to exit the runway he lost all brake pressure in the left brake resulting in a mushy brake and fully depressed and attempted to use full left rudder to regain directional control. Students right wheel went into the grass and back out on to the taxiway where he was able to gain control and pull the mixture shutting the engine down and securing the airplane safely without any damage to student or aircraft. Instructor has been his full-time instructor since he became a student and student had just successfully completed a stage check the day prior demonstrating proper PIC abilities.