In science fiction you get neutronium which supposedly makes darn good armor--which of course has absolutely nothing to do with reality.
You hook up your Acme star spinner (pay no attention to the energy needed) and spin the star up so the surface gravity at the equator goes negative and start picking up the pieces.
At first you're going to get the normal matter that was on the outside, but once that's gone what happens? With the pressure removed it's obviously going to change state, but into what? Simple decay to hydrogen? Given the density this doesn't strike me as the right answer. Does it fuse to the lowest energy level, yielding iron and nearby elements? Given the neutron density do we get a massive r-process capture, giving us a radioactive hell of row 7 elements?
Edit: Based on what has been said so far I realize I'm not really describing it right.
The deepest parts of the surface matter obviously get quite a neutron flux and get pushed down the table and since there can't be solids at that point you will have mixing, it will push at least the denser stuff down the table at least to bismuth. How far into the surface that neutron flux goes would say how much of it gets converted.
The issue comes down to how fast that conversion happens. On a long enough time scale you get the sort of stuff that's thrown off by neutron stars going splat (but does that actually contain a bunch of stuff past bismuth that decays before we see it?), but what time scale is that? As we pull off fresh stuff how far along the process does it get?