That would be something of an advantage, no? The metal particles would be mixed with water still, pulling along some of the stream. The tighter the "beam" of metal particles, the better - presumably that allows a more precise cut.
No, because you also need to increase the pressure of the water for it to cut. The nozzle increases the pressure of the water by constricting a constant flow into a smaller area, which increases the kinetic energy of the water and the abrasive particles.
A magnetic pinch would (I expect, I only really covered them a bit in a plasma physics course so I'm not an expert) basically pull all the suspended iron particles out of suspension and compress them into a thin rod, without actually compressing the water very much. My hunch based on semi-informed knowledge is that it just wouldn't do much to actually cut anything, but I could be wrong.
The other problem is that magnetic fields also produce a lot of heat in a conductor. The metal particles that clump up would probably sinter together or even melt. On top of that, it'd take a lot of power to run... pinches aren't super efficient.
