Tile that is made of stone or a stone-like substance can be fairly difficult to cut through because regular saws will either overheat or kick up a truly impressive amount of dust -- which can, in turn, gum up the saw and damage your lungs if inhaled. A few types of circular saws, however, are designed for this kind of cutting. Specifically, "wet" circular saws have special blades and a system of water sprays that coat the tile with water to prevent overheating and minimize dust.
Things You'll Need
Wet circular saw
Measure out where you wish to cut on the tile. Make a mark on the edges of the tile to show where the blade needs to start cutting.
Draw a line between the marks, using your straight edge as a guide.
Lay your tile face-up across the sawhorses and use your clamps to secure it in place.
Line the saw blade up with the marks on the tile. If necessary, adjust the blade height so that the blade will cut all the way through the tile. Turn on both the blade and the "wet" system. Make sure your blade is not touching the tile when you turn on your saw.
Guide your saw slowly and carefully into the tile. Do not try to force the blade to move faster, as doing so can damage your tile.
Continue cutting, using the line you drew in step 2 as a guide. Do not try to twist the saw blade to the side, as doing so may damage your saw and mar the tile.
Don't try to cut tile with a non-wet blade or saw, as this will damage the tile, your saw and possibly your lungs.