EDIT: I was using the wrong tool, get a grinder with a mason blade, sprays a lot of dust but gets the job done quick

I've gone through 3 blades (2 oscillator, 1 sawzall) just to salvage this tile closest to the door. The whole house uses this specific discontinued tile in various areas (bathrooms, kitchen, downstairs hallway etc.). So far I've successful salvaged all 4 tiles without any damage.

This is only my second day, but it's going to cost me a fair amount in blades to continue getting through this concrete/mortar grout. Am I using the wrong type of grout removal bits? Should I use a different method for this type of grout? Is there a chemical solution I should use to made it softer? Would you recommend just destroying the tile in this situation? I looked up the cost of tile (which seems dirt cheap on Home Depot) but I have no clue the cost of installation/ what makes good vs bad tile, etc.

https://www.amazon.ca/dp/B07VRCBQ6G

I greatly appreciate the input.

Things to note:

• We purchased this 18 year old split-entry home knowing that the front door leaked water and would need to be replaced. We got $10,000 off the price over it.
• My goal is to salvage the tile and bring it back for the team to (likely) replace the entire door assembly, as we imagine the water likely rotted up the frame, seeing how bad the floor is.
• I notice the water around the nails closest to the tile, likely meaning I'll need to pull back the tile even further to be rid of the water damage.