Depends on what you mean by “empty”. The protons and neutrons which contribute most of the mass of ordinary matter take up very little space, but the electrons are not so well-defined. And all of the space between the protons, neutrons, and electrons is filled with electromagnetic fields. It’s hard to say that’s “empty”, since it’s those electromagnetic fields that give things what most people think of as substance: When you push on an object, what you’re feeling is the fields. And for that matter, even the protons, neutrons, and electrons are themselves manifestations of fields.
But more to the point: Almost any substance will compress and become smaller, if you put pressure on it. However, liquids and solids will only compress by a very tiny amount under pressure. The water at the bottom of the Marianas Trench (which is under a great deal of pressure) is, if I recall correctly, less than 1% denser than the water at the surface. Gasses, on the other hand, do compress readily under pressure. If you have a piston full of gas, and double the pressure on it, the gas will only take up half as much space as before (assuming the same temperature).
Normal matter–that is, atoms and molecules-- is mostly (or depending on your interpretation, all) empty space. The “empty space”, however, is filled up with electromagnetic fields that repel each other. See this thread: [thread=299054]Why can’t my hand go through my desk? (physics question)[/thread]. (And ignore the audio wizard guy who explains it all via “common sense”.)
FWIW, I used to work at the UMR Rock Mechanics and Explosives Research Center (though not in the High Pressure Water Jet Laboratory). I did get to see this technique in action a few times. The waterjet method of cutting has many advantages; it’s self-cooling, it doesn’t require sharpening or predrilling, it doesn’t result in slag or heat affected zones in the material, it’s properties can be easily modified by changing the nozzle or adding abrading constituants to the stream, et cetera. It is not, as has already been explained, anything like a laser, though. “Coherency” with regard to water (i.e. keeping the stream from diverging at the nozzle exit) is entirely distinct from coherency in light, which indicates that the photons/waves have the same momentum and energy properties. (Note that coherent ≠ in phase as is often incorrectly stated; merely that the interference pattern is unvarying wrt time.)
A minor nit: It is the high velocity of the water that facilitates the cutting. Once it leaves the nozzle, the static pressure of the water is at near atmospheric. The high pressure feeding the nozzle is a convienient means to create the high velocity. “A device that converts fluid pressure to velocity” is a sensibly good definition of a nozzle. (the dual of which is known as a diffuser)
Another means of creating similar velocity with modest pressure is to create a vacuum, and allow ambient pressure to accelerate the water into the void. This process (called cavitation) is easy enough to accomplish that it frequently occurs unintentionally, and is responsible for the erosion of boat propellors, and is the mechanism that creates “pot holes” in the bed of streams that carry swift current.