Yes, it can be cut, but you'll lose the shaped edge, as I'm sure you're aware. The cleanest cut would be from a wetsaw, but you could do it in varios ways. You'll need to cut the backsplash(s) as well, or at least probably. If you are going to only have one side splash, you might be away with taking the 1" off one end, rather than 1/2" on both. A drycut diamond blade on a circular saw would be dusty, and probably chip some. A diamond cup wheel on a grinder would give a clean cut, but making a straight line is harder. A couple of companies make what amounts to a small circular wet saw that should work well. You'd probably find clamping a straight-edge would give a nice clean cut. A conventional wetsaw could do it as well, but most don't have a long enough bed to do this in one pass. The thickness isn't really an issue. If you get the blade pinched or cocked, you could end up with a jam, and split the slab. If you take it slow and easy and keep things straight, it's no bigger deal than cutting a piece of hardwood with the right diamond tool. Keep in mind that the opening may not be perfectly square.
Another option is to notch the drywall and slide the whole thing in place. Well, you'd probably have to take a small section out on one side and notch the other. Patching the drywall afterwards would be much easier and safer than cutting the slab, let alone having to buy the tool to do it.