ZZZ TRACON Controller reported observing Aircraft X off RNAV track and altitude while Pilot recovering dropped Electronic Flight Bag; resulted in an MVA violation.

Narrative

Aircraft X checked in with me; working the final sector; direct a fix on the RNAV XXR approach that we do not normally send aircraft to. They were direct that fix to go behind an unidentified VFR target. Because of this I pulled up the approach plate on the ACE-IDS above me to make sure I was giving a correct clearance and could ensure the aircraft was flying the approach correctly. I cleared Aircraft X to cross ZZZZZ at 5000 ft. and cleared for the RNAV XXR approach. The Pilot read back correctly except he read back Runway XYR. I reissued the approach clearance to clarify the assigned runway; since there is no XY at ZZZ1. The pilot again read back Runway XYR and I verified that he was landing XXR at ZZZ1 and he corrected to the correct approach and runway. Aircraft Y checked in on the downwind and I gave a vector for Runway 30 and altitude of 5000 ft. expecting to turn base over top of Aircraft X when he reached ZZZZZ1 at 3400 ft. I descended Aircraft Y to 3400 ft. when I meant 4400 ft. and didn't catch the readback because it was what I had said and I was starting to notice Aircraft X doing something out of the normal. I noticed that Aircraft X was not tracking at ZZZZZ2; and looked up to confirm with the plate; then asked the Pilot to verify he was still on the approach. As he was responding to this query I saw he was continuing his descent below the MVA and next fix on the approach. I immediately issued a low altitude alert; canceled the approach clearance and climbed the aircraft to a safe altitude. I noticed that Aircraft Y was descending past 4400 ft. and so I turned south to go behind the climbing Aircraft X. I asked the Aircraft X if he had the field in sight for a visual approach to which he said no and then responded in the affirmative so I cleared him for the visual approach. I also cleared the Aircraft Y for the visual approach also.After speaking with the Pilot; the Supervisor reported the aircraft had been looking at his iPad and when I asked if he was tracking the approach; looked up and dropped the iPad; in retrieving it the airplane dived and the low altitude alert gave him the alert needed to climb the aircraft to a safe altitude. [Recommendation:] there were multiple contributing factors but none that could be changed due to the split second decisions that happen every day.