C150 Flight Instructor reported a gust of wind while taxiing resulted in student lose of control with a taxiway excursion.

Narrative

On Day 0; between approximately XA:08 and XA:10; Person B and I began some advanced taxi practice southbound on the taxiway at ZZZ after spending time in the empty ramp parking area. As we taxied; an apparent gust of wind from behind may have caused the aircraft to shift leading to Person B steering the aircraft more towards the right. Though guarded by myself; the action happened too quickly and the aircraft departed the paved surface onto the grass and slid down towards the muddy area on the downhill. I immediately shut down the engine as the aircraft began to slide. There was no contact of the propeller or any of the aircraft airfoils or control surfaces with the ground. Only the left main gear was bogged down in the mud. Person B and I tried to reposition the aircraft so that I could try to taxi it back onto the paved surface but to no avail. We subsequently called the FBO and was able to safely two the aircraft from the muddy area. Person C; A&P IA (Inspection Authority); assisted with this task and we were able to safely taxi the aircraft back to their hangar to remove the wheel pants to clear the mud from the aircraft. The aircraft was safely flown back to ZZZ1.