If you have replacement tiles from the same lot, it will actually be easier and less expensive in many cases to replace the tile, with confidence that the tile will blend with the tile on your floor presently.  If you do NOT have replacement tile from the same lot, you will find that even though you have purchased the some type of stone, and perhaps even gotten it from the same quarry, the color will likely be off subtly.  Not enough of a difference to notice in the store, but once the tile is placed on the floor you will be able to pick it out. 

If you cannot remove the stain, replacing the tile may prove to be a cost effective option.