Air Traffic Controller reported aircraft unable to climb due to experiencing a TCAS RA resulting in the aircraft flying below the MVA. ATC issued vectors to the aircraft to be sequenced to the airport.

Narrative

Aircraft X was on a visual approach XXR; Aircraft Y was on a visual approach XXL. I had them paired both maintaining visual separation. Aircraft X got a TCAS-RA so I asked if they could continue. Aircraft X decided they needed to go around; now they are at 014; below my MVA of 026. I told them when able to climb and maintain 040. They advised me that their TCAS would not allow them to climb and wanted them to keep descending and they needed a vector to the right to climb. I had to bring up my map and give them [priority] vectors to the right to climb. At this point I also had to call ZZZ and stop departures as a right turn put Aircraft X into the departure corridor. Recommendation - We are seeing more and more TCAS-RA go arounds than we have ever seen at ZZZ. I have worked this final for 15 years and have never had this many TCAS-RA go arounds. Something has changed in the airline industry that is affecting us making good sideby pairs. The increased go around are increasing out rate and workload as well as causing more risk into the NAS. An event like this one is very dangerous as the plane was so low and really; I had nowhere to go. I am just lucky that ZZZ did not have a plane rolling for takeoff when I called them. The change to the TCAS needs to go back to how it was before; or the rate should change at ZZZ for us to stagger all arrivals.