Diamond cutter is producing large amounts of carbon dust which is very harmful, so I am in search of an alternate method to cut a laminate without causing damage to the laminate.
There are several possible tools for your problem (for instance: water jet and laser jet cutters), but the majority of manufacturers cut with rotary tools or straight blades. In rotary tools, an alternative to diamond cutter is the use of a "tungsten carbide" cutter, which allows to cut composite parts quicker, and with less heat generation. Perhaps, you could test this possibility for cutting your composite pieces.
After a piece has been cut, it is recommended to use Perma-Grit sanding blocks or hand tools to clean up the piece edges. For more details, see: http://www.fibreglast.com/product/composite-laminate-cutting/Learning_Center
There is an excellent video about composite cutting: "How to Cut Carbon Fibre Sheet and Carbon Fiber Parts (Technique & Safety), in the internet site https://www.youtube.com/watch?v=EWzN6GZeEzs.
If you are concerned about carbon dust, one solution is to wear adequate protective clothing and work in a well ventilated area. If only straight cuts are required and the laminates are relatively thin, water cooled diamond cutter table saw such as those used to cut tiles or mineral products also work well. The water cooling has the additional advantage of drastically reducing the airborne dust. This is what is often used for making material test samples, although one need to be careful as the tolerances on such cuts are relatively large..
A milling machine can be used for complex cuts, but tools are quite expensive and have a very short life, not to mention that the dust problem is not solved with dry milling and that sometimes spindle speeds may also be quite high. I've personally found that polycrystalline diamond coating on straight flutes end mill worked good and minimized delamination by reducing the axial cutting load. I've seen some other specialized serrated cutters do really well for aeronautic parts.
Wter jets not only produces edge delaminations, but the cut is often not perpendicular to the part and the thicker the part, the worst the problem. However, if I recall correctly, water jets with abrasive suspensions do work better.