The problem with your situation is that your underlayment is probably either plywood (Doubtful, but possible) or more likely, it is particle board. In either case, the thickness of the underlayment is too thick for a layer of tile on top, (there would be an elevation transition) of the thickness of the tile. Think about walking into your kitchen in your bare feet and stubing your toe on the tile edge. OUCH!!!!
What's more, the grout for your tile is NOT waterproof. As the floor gets wet, the water penetrates and swells the particle board, then guess what? Broken or cracked grout and tiles, and a new home improvement project.
The right way to do this is to cut out the underlayment in 1-2' square chunks using your skill saw, and ADJUST IT TO ONLY CUT THE UNDERLAYMENT< NOT THE SUBFLOOR!!!!!
Then install a cementitious backerboard according to the instructions of your tile manufacturer. This board is stiff, and should help avoid cracking and swelling. Most backerboards are only 1/4" thick which will allow a proper floor elevation without transitions.
Read on this board regarding tile by searching (ctrl-f) then put "tile"in the search box.