A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements.
Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.
When they are combined they create a material which is specialised to do a certain job, for instance to become stronger, lighter or resistant to electricity. They can also improve strength and stiffness. The reason for their use over traditional materials is because they improve the properties of their base materials and are applicable in many situations.
Corian
Corian is a composite of acrylic and minerals used in worktops. The laser vapourises the acrylic and leaves behind a fine white dust. While Corian can be both laser cut and engraved, you should be concerned about the volume of abrasive dust left behind.
Magnetic Sheet (non-chlorine)
Magnetic sheets cut well, leaving a clean finish. But make sure you choose a variety that does not contain PVC or Chlorine.
Fibreglass
It’s not possible to laser cut fibreglass as it’s key ingredients, namely, Glass and epoxy resin either cannot be cut or give off toxic fumes when reacting with a CO2 laser beam.
PCB (FR4)
FR-4 is a composite material composed of woven fiberglass cloth with an epoxy resin binder that is flame resistant (self-extinguishing). A CO2 laser is not able to cut FR4 and will severely char the surface. A high power fibre laser can cut FR4 but some charring still occurs, which is unacceptable for many applications. Fibre laser cutting of FR4 is best left to cutting the retaining tags on multi-panel boards.

Epoxy C21H25ClO5
You should not laser cut or engrave any composite that contains Epoxy resin. Epoxy resin contains Chlorine and emits toxic fumes.
Coated Carbon Fibres Polyacrylonitrile (C3H3N)n
You should not try to laser cut coated carbon fibres as it is a combination of a carbon fibre mat, which can be cut with some success but there is an epoxy bonding agent which gives off toxic fumes when burned.