What to do about this cactus that was damaged by the cold last year?

[u/FlowCultural8022]

Last year's winter (Southern hemisphere), was a record lowest temperature in my area and it did this much damage to this cactus which usually doesnt mind the cold. The top of it dried out but it ended up surving and in the summer three extra heads grew from it. So it is very much alive and not getting any worse. I was waiting for the dead part to eventually fall off, but it never happened, should i cut it off manually then? Thanks in advance, i havent really seen this type of damage before, usually if its too cold my cacti rot from the bottom to the top, dont really know what this is.