Usually a hard materials such as silicon carbide, alumina or silica is used as the abrasive compound.

Cutting disc used on angle grinders and drop saws use a very hard and strong wearing matrix to bind the abrasive compound to form a disc.

Water jet cutters use a high speed jet of pure water created by first pumping the water to very high pressure and then feeding it through a very small nozzle.

Water jet cutting can work on nearly every material be it wood, stone, metals, carbon fiber reinforce polymer (CFRP) sheets, foam and ceramic tiles. 

All abrasive cutting methods will be expected to leave a heat affected zone (HAZ).