This video may help https://www.youtube.com/watch?v=I0Gm1iG6-XA
You need to take a chisel and hammer to get some more of the grout out around the broken tiles. Once you've done that, use a wider chisel or heavy duty scraper and hammer to get underneath each tile to knock it away from the thin set. You'll have to remove as much thin set as you can so you're able to put new tiles in place. Be patient and go slow so you don't damage other tiles.
At any home improvement store in the tile department you can buy a small hand tool called a grout saw. It's only about $10. Use this to remove the grout from around the damaged tile. Then it will be relatively easy to pry out the bad tile. Broken tiles are EXTREMELY sharp, so wear safety glasses, gloves and long sleeves.
Do you have any photos?
Here you go https://www.housebeautiful.com/home-remodeling/diy-projects/a25858233/how-to-repair-cracked-tile-grout/
Hopefully you have leftover tiles and grout. Remove the grout, pop out the busted pieces and mortar, put in some new mortar, the new tile, then grout.
Hi Everett, hope one of these helps,