You really only have one choice. Pop up the cut tiles and replace them with new ones. This assumes that you can find tiles that match.
- Cut the grout lines around all tiles.
- While wearing safety glasses, pry up the cut tiles.
- Clean the subfloor of old mortar as best you can.
- Apply new tiles (Yes, I'm hand waving! - how to do this is readily searchable).
- After about 24 hours, fill the gaps with grout.
Depending on how you are going to finish the exposed wood, you may be able to avoid replacing the tile on the bottom right if you cover it.
EDIT (After further photos).
I stand by my answer on the right side, but and totally stymied by the left. And the angles just make it worse.
At this stage, I'd look at replacing the entire floor as the correct solution, which is a lot of work. You may wish to hire an experienced professional.
- Fill the gaps with mortar or any old tile of appropriate thickness., and carpet the whole area.
- With a tile blade on a circular saw and a good straight edge, cut out the the affected area, and redo with another tile, creating a transition zone of contrasting colour and angles. However, the cut edge will be a bit sharp. You may want to install transition strips.
- Rebuild the wall.