When the (professional) installers did our granite in the kitchen, they used angle grinders with diamond blades, dry, to make all the necessary on-site cuts. For polishing they had angle-grinder mounted diamond polishing pads in 3 grits that they used to polish any exposed cut ends.
The holes for the faucet and accessories are pre-cut about 90% of the way at the factory - from the bottom. They just used a hammer to knock out the holes that were actually needed (we skipped the unnecessary dishwasher airgap and soap dispenser).
A saw shoe is not going to scratch granite. As they told us, you can cut all day on the stuff and the only damage will be to your knives. They use a contrasting color paint pen or grease pencil to do layout lines. For long straights if you use a circular saw, you probably want to clamp down a straightedge anyway instead of trying to see a line thru the dust.
