It should. I usually have to sand the edges clean after cutting with a saw. FR4 board sands nicely. If you want, the board can be snapped apart if you put a deep score in it with a Dremel, but you need to get at least halfway through it. Or you can just cut it all the way through with the Dremel. You can do pretty much anything you want in terms of cutting, grinding, and sanding the stuff. It's a pretty amazing material actually, it's an epoxy-fiberglass composite.
Some of the protoboards use a cellulose based material that's quite a bit softer than the FR4 so you may be dealing with that. It cuts and drills more easily than FR4, but it tends to chip and split so you have to be more careful with it. I despise circuit boards made of that stuff. The Chinese always use that crap material for circuit boards. It baffles me why they do it since FR4 is not expensive by any means. It's like they're cutting costs to the point of ridiculousness.
