Water jet cutters use an abrasive sand (like garnet) to do the cutting. The water itself is just the medium that carries it at high velocity in a focused stream, to do the cutting. If it were just pure water with no mineral content at all, it wouldn't work as such for cutting hard materials. Even tap water contains some mineral content, which would be abrasive enough to cut plastics & other soft materials at high, focused pressure. And the velocity itself plays more into the 'cutting' action - perfect example is a 'soft' lead bullet penetrating a much harder steel plate at high velocity.
And some ropes & other natural fibers are known to contain a high amount of silica (the same stuff sand and natural sharpening stones are made of), which is why such products induce wear on the machinery used in manufacturing.
And brittle carbides and brittle steels & glass, etc, can still be finely cut by materials harder and sharp enough to do so. This is what allows very fine abrasives like diamond to precisely shape, thin and polish an edge on a knife in a carbide-rich steel - all done at light pressure as used on a polishing strop, for example. And it will do that job better than an abrasive which is only capable of fracturing the carbides under pressure.