Well part of it could be induced during cutting, but more likely the part is magnetized before hand and by cutting you are just relieving this. If I have a large block that that has no net field that doesn't mean that it is not magnetized, just that the fields balance out. When I cut it up that is no longer true.
Buy yourself a simple AC demag coil and keep everyone happy.

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Plymouth Tube

We have invested in a demag device which I have used with varied success. Be aware that the incoming material before cutting are large slabs and not small pieces. Those incoming slabs from the steel mill show little mag. How does the sawing action induce magnetism? Annealed material does not display any mag after sawing but prehardened alloys are the problem.

The difference in HT condition is related to properties. Annealed steel retain very little magnetic field.
Also in the hardening process steels tend to develop a preferred magnetic orientation.
Your large plates are loaded with small internal areas that are magnetized, and it is a material that retains field well. When you cut them apart the fields are now unbalanced and can be measured.

I remember the drill, cut the block and demag, finish grind and demag, trial fit the die blocks, take it apart and demag.
Often before finish grind we would re-temper parts in an effort to minimize the fields. Sometimes it helped.

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Plymouth Tube

So you are saying that the mag develops from hardening but these fields are balanced within the microstructure and do not show to any extent in the finished slab as supplied from the mill? I have never heard of a hardening process (quench and temper) also inducing magnetism. Is it because of preferred orientation of the hardened structure?

It is called a stain-induced magnetism. Basically, the stain created by sawing will change the Fe-Fe nearest neighbors, or change the atomic distance. the ferromagnetism in your case will only occurs at the surface area, so if you can remove the surface very gently you will be good, or just do a stress releif anneal.

I got couple of papers published on that. check with these if interested:
"Giant strain-induced ferromagnetism in Fe59Mn17Al24", Philosophical Magazine, 2011, 1–12.
"Magnetic properties and thermal ordering of mechanically alloyed Fe–40 at% Al", Intermetallics 14 (2006) 396–405.

Yes, I agree that it is a surface condition. I have learned to demag via a "scrubbing" technique rather than coil wrapping because of the wide swings and inability to split the poles with a demag coil. I will investigate strain induced magnetism. Thanks!