To be EXTRA safe, plug the saw in to a GFI outlet either in your kitchen, garage or basement. Most kitchens SHOULD have GFI outlets - you know, the square outlets with the test buttons.
You should be plugged in to a GFI regardless - remember, when you work outside you are probably grounded and could be the path of least resistance of a short to the ground. This is why codes require GFIs in basements and outside.
Here's the thing: cutting concrete is a nasty, loud, sparky and dusty endeavor. I was reminded of this last week using my angle grinder with diamond blade to cut some 1 and a half inch thick granite for a friend.
At first I was like "Jesus, this is going to take forever" but once I got my technique down it went fast.
You need to concentrate on one spot and get a "bite" or indentation in the concrete and work out from there. It seems once you get the bite, the saw blade cuts better when is engaged in a smaller surface area.
For me, getting the bite and drawing the saw BACKWARD works best for me. The saw naturally wants to pull forward due to the blade spinning forward. Start about a foot or so forward, getting the "bite"then draw the saw back to even out he level - then repeat.
The concrete saw, if you go that route, will be the same. If all you do is make light passes back and forth you will just polish the concrete.
Using a skill/circular saw, I would probably set the blade guard to about a half inch or maybe a little more, hold the spinning blade in one spot till it digs in and then proceed forward (or backward in my case) to cut across the concrete to the end. Repeat by increasing the depth for each pass until complete.
I'm going to be doing some granite work this weekend helping a friend. We purchased some granite remnants and will attempt to make a few tops for a vanity and laundry sink. I purchased a variable speed wet grinder and diamond polishing pads. I have a single speed grinder but polishing requires a slower/variable speed. I will be working with water and electricity BUT the grinder comes with a built in GFI.
Wish me luck. And good luck to you.