A TRACON Controller reported an aircraft descended below their assigned altitude and flew below the MVA.

Narrative

I was working Approach/Departure when I took the handoff from ZZZ1. The aircraft checked in with me level at 10100 ft. with information Tango; aircraft was established on VXXX. Once the aircraft was fully inside the 9600 ft. MVA I instructed the pilot to 'descend at pilots discretion maintain 9600'; the readback from the pilot was a little broken but I heard 9600 in the read back so I didn't ask him to verify the altitude for me. Around two minutes after I had given the descent instruction I noticed the aircraft at 9300 ft. in the 9600 ft. MVA and asked the pilot to verify they were level at 9600 ft.; they responded that they were at 9300 ft. and descending. I then instructed the pilot to maintain 9600 ft. and received the appropriate read back from the pilot. Around two minutes later and once the aircraft was at the MVA of 9600 ft. I gave the pilot a vector to 360 for the visual approach to Runway XX and a couple minutes later the aircraft had the airport in sight and landed safely without incident. If I receive a read back that is not completely clear I could go back and ask the pilot to verify the instruction. With a mountain to the south of the airport we usually have a little static with communications with aircraft that are in this area and below eleven thousand feet so asking a pilot to verify an instruction might help clear up and confusion.