Dealing with Neutronium has some rather startling consequences, such as it being a massive explosive when released from the immense gravitational pressure holding it together. In addition the environment around neutron stars is pretty dramatic. There are immense magnetic fields, beams of charged particles coming from the magnetic poles and tidal forces due to the immense gravitational field concentrated in a very small area which would stretch you out like a piece of spaghetti.
Schematic of the magnetic field and particle beams surrounding a neutron star
So setting down your lunch box and punching into the worksite at the Neutronium mine is going to be rather challenging.
Since the neutronium is both held together and stabilized by the intense gravitational field of the neutron star, you will need to counter the gravitational pull of the star, yet somehow keep the neutronium compressed in a usable fashion. Sadly the best way of destroying a star to retrieve bulk elements from the core is to detonate a type 2 Supernova, but that requires the nuclear fusion reactions in the star to run up the curve of binding energy from Hydrogen to Iron. Once there is no longer any fusion energy from the core (Iron neither releases energy from fusion or from fissioning) the remainder of the star collapses from gravitational pressure and the core implodes. The neutron star might be the remnant of the Supernova event, so there is no energy available to break the star apart.
This means external energy must be applied, and since the gravitational energy of a star is so immense, the energy required to overcome this must be at least equal to the gravitational binding energy, and ideally greater in order to allow the material to be flung free of the worksite. The only plausible way would be to crash another neutron star into the mined star at a high velocity, or to bring the neutron star close enough to a black hole to have the gravitational energy of the black hole rip the neutron star apart, where the neutronium then spirals into the accretion disc. (How you retrieve the neutronium from there is an exercise for the reader....)
The other problem really has no solution with known or plausible physics. The Neutronium will decay because there is no strong nuclear force to bind them together and the gravitational energy that kept them bound and stable has been removed. The Neutrons will rapidly decay as per the initial link, and there will be a blaze of energy as the neutrons are converted into a proton and electron:
So perhaps the best advice to the would be industrialist is to leave sleeping neutron stars lie...