Neutron stars are incredibly dense. I mean incredibly dense, its unimaginable.
Imagine our sun, its huge and its very dense. However if we compress it down to the density of a neutron star, it would only have a radius of 20km. Can you imagine that, 20km! Down from 695,700km.
So why is it so dense? There is a long write up for stellar evolution and how it all works, but for a neutron star the mass is large enough that all the protons and electrons in the star are compressed down under gravity so much that they join together and become neutrons. Before this a thing called electron degeneracy holds the star density however when the mass is over 1.4 solar masses and there is no fusion in the core countering the downward pressure of gravity , the star collapses into a neutron star
Anyway lets move on to what would happen with this teaspoon of neutron star.
Its not like you re going to be able to carry this round with you. A singe teaspoon would weight on the scale of 10 billion tons ( a mountain).
So you have a teaspoon of substance you cant move, but not only that, without the presence of the rest of the neutron star the pressure gradient between it and its surroundings becomes horrible news for anything around it. Lets assume you can contain this in a large building. The teaspoon of neutron star, without the rest of the neutron star, explosively expands. The pressure inside the building would be on the order of a quadrillion times the atmospheric normal. It would be like a VERY VERY dense rock (order of ten million times the density of a rock) materialising inside the building. Destroying everything inside the building .
So try not be in the area of a piece of neutron star in a house, it wont end well.
We've not even got to the worst bit. Now following from what i said before, that protons and electrons are forced to create neutrons. Well without the gravitational pressure of the neutron star the neutrons start to decay. Like a nuclear bomb.
As the neutrons decay they lose mass, this mass is expelled as energy. Giving off 10^27 Joules of energy, roughly the same as 50 trillion of the first nuclear bombs made. It is enough to literally rip the earth apart.
So if you are going to collect some of a neutron star, please do it quite a way away from the rest of us.