I think I would be checking out a stone mason to see how difficult this might be . It looks like it goes under the facing on the wall which could be drywall or some kind of plaster . Is it possible to have mantel built that could slide over that sort of like a box in a nice wood .

It's not necessary to remove the mantel. Do a google search for "Fireplace mantel slip cover". Much simpler.

If your would mantel will be more substantial than the stone one it should be ok to mess up the sheetrock a little. A sawzall should be able to cut through the sheetrock above and a pry bar used below to wedge it out.

i’d also be tempted to just cover it as @partim recco’d - there are tons of these on Etsy