That's mud-set tile. Almost a lost art today. I had to dig out my shower faucet through the same stuff. I lost more blood than tile. When replaced the tile, I used plywood covered with tile board in just the area I cut out. If you are going to put in tile to replace it, you want to find a tile installer that knows how to set tile in mud. There are still a few around.
Edit: BTW... that isn't standard cement. Its a special mix of sand and portland cement and I really don't know much about it other than you don't use Sacrete. I really doubt you are going to be able to use that existing bed of mud to replace the tiles too. You are probably going to have to remove it all and replace it or remove it all and replace it with layered tile board (much easier and more appropriate for a DIY project, I would guess).