The building that I live in is several hundred years old. Older than the United States of America. And it is solid as a rock because, like practically every building in Italy, it is constructed of cement and stucco.
This, then, is how you replace a tile floor in such a structure:
This is in a room that is a couple of floors above street level. Apparently the subfloor is thick enough concrete that you can jackhammer a couple of inches into it without compromising the overall structure!