Dig out the grout with your grout saw on all sides of the tile that you want to remove. Work with the saw in small sections of grout, scratching off the surface first and then digging down into it. Vacuum up the crumbled grout as you go so you can see into the bottom of the line. Continue digging until you've exposed the line where the tile meets the underlayment.
Work your putty knife into the line where the tile meets the underlayment. Move all along the length of it on one side, gradually working the knife under the mortar; then do the other sides. Don't force the tile or try to pry it out; work it little by little until enough of the mortar is loose that the tile pops out.
If working with the putty knife by hand doesn't get the tile out, hold the blade edge flat against the line where the tile meets the underlayment and very gently tap the back of the knife multiple times with your hammer. If the tile doesn't respond on four or five taps, reposition the knife and try again until it does.