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?
Best Answer
This is not really mining, as the neutrons and protons and electrons in the inside of a neutron star recombine to give you nuclei when the pressure drops to zero. The solid crust of a neutron star contains (very heavy) neutron-rich nuclei arranged in lattice domains. At the interface between the core and the crust you have the so-called pasta phase (highly deformed nuclear clusters). All this stuff is comprised of neutrons and protons (the fraction between the two changes as you go deep, increasing the pressure). Charge neutrality is guaranteed by a sea of relativistic electrons, more or less like in a metal, but with a lattice of exotic heavy nuclei. Differently from the terrestrial solids, these neutron-rich nuclei are fully ionized.
The thumb rule is: as you compress, proton and electrons combine to give more and more neutrons. Finally, after the pasta you reach the core: this is a homogeneous fluid comprised of protons, neutrons and relativistic electrons (homogeneous cold catalyzed nuclear matter). This makes sense: the nuclear clusters are so compressed and close that they merge together in a homogeneous fluid. Some muon may appear (the exact density at which this happens is debated and depends on the still unknown details of the nuclear strong force). As you go deeper and deeper things are uncertain: you may find hyperons, a quark-gluon plasma, or other exotic stuff (we really do not know).
All this stuff exists because of the pressure and temperature conditions in a neutron star interior: remember that (differently from the atomic nucleus) a neutron star is held together by gravity, not by nuclear forces (nuclear forces create the pressure needed to sustain it against gravity). So, when you spin a neutron star up, you also change its density and pressure profile, changing also the composition (beta reactions take place).
In general, catalyzed nuclear matter has the tendency to recombine to give you the "usual" elements when you lower the pressure (or density): as @rob pointed out in the comments, this is well studied because of neutron star mergers (part of the matter is ejected and gives you metals like gold, platinum and many other elements.. this is called kilonova).