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.
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.