Does your material have to stay on site? A shop that machines large quantities of stone or glass will have saws and/or waterjets that are designed for cutting ceramics and related materials (some "engineered stone" for countertops is nothing more than quartz bonded with filled polyester). For large quantities a CNC saw would work better but there is no reason a manual saw won't work.
The saws use large quantities of coolant water so materials stay cool. When you keep the matrix cool, composites act pretty much like ceramics. The water on a stone saw is normally recycled, so it normally somewhat alkaline from stone dust. Waterjets require clean water, so their water source isn't normally recycled. It normally comes from the municipal water supply so it is quite clean.
A saw will leave a finish that is very smooth (quite often when they are fabricating a granite counterop they can simply polish the sawn edge). If the saw is set up and operated properly it will give you cuts that are dead on. I don't recall the feedrates they use on a saw, but I would be surprised if they were less than 300mm per minute. They move right along. Kerf is normally about 1/8".
Waterjet feedrates vary big time depending on the operating pressure, but will be much slower than a saw. The edges are fairly straight and smooth, but it depends on various factors. The edge won't be even comparable to the smoothness of a saw cut, however. Kerf is typically around 0.006".
Because of the housing slump, many stone shops are hurting for work, so they would likely to be anxious to talk to you. Larger shops are more likely to have the CNC equipment, so you might call Home Depot of Lowes and see who makes their custom granite countertops. Or if you don't need huge quantities keep your local stone or glass shop in business.