Furthermore, since garnet has specific refractive properties different from other materials, could we pass all ferrous grains through an extremely high-speed discriminating chamber that looks for these properties in each grain, and magnetically directs the garnet grains back to the abrasive holding bin to vastly increase the recycling, while all other ferrous material goes a separate bin (for waste or other recycling purposes)?
I do love the idea of a Rail gun cutter, though - just not sure how it could really help cut things.
It's a good idea though.
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.