Slime is a non-Newtonian matter because it doesn't seem to follow Isaac Newton's definitions of the three states of matter: solids, liquids and gases.
Slime seems to pour, or run, like a liquid. But much more slowly than water. And when it is punched fast, it feels hard like a solid.
A non-Newtonian fluid is a fluid whose viscosity is variable based on applied stress or force. The most common everyday example of a non-Newtonian fluid is cornstarch dissolved in water.
Behavior of Newtonian fluids like water can be described exclusively by temperature and pressure. However, the physical behavior of non-Newtonian fluid depends on the forces acting on it from second to second.
Other examples of strange non-Newtonian matter are, jelly, blood, toothpaste, ink, ketchup, yogurt, gravy, and pie fillings.
You can classify slime even further into a group of substances called sheer-thickening fluids. These fluids get thicker when pressure is applied.
Of interest, find out what happens when you shoot a golf ball at a balloon filled with non-Newtonian fluid by watching this video.