Textiles can usually be sliced with scissors or knives. These devices work by concentrating massive shear forces on tiny areas, which causes individual fibres making up the textile to sever. If you attempt to cut some textile with an insufficiently sharp knife, the fibres will bunch around the blade, and will be dragged through the textile. If you attempt to cut some textile with a poor pair of scissors, the blades of the scissors will tend to be pushed apart so the efficacy of the scissors is decreased.
So the idea is to have a material which causes the tools used to cut the material to become blunt.
The material is a composite 'sandwich', with outer layers of conventional woven or non-woven fabric, surrounding a core layer of hard fibres, of varying lengths and thicknesses, embedded in a viscous, sticky material. The outer layers provide the usual strength of the fabric. The inner core provides the slice resistance.
Possible hard fibres include glass fibres, carbon fibres, aramids, or fibres of various metals. Possible viscous materials include tar.
When a knife attempts to cut the fabric, the hard fibres will tend to be pushed by the blade of the tool within the viscous material, rather than being severed by the tool. The fibres will bend and adhere to the blade.
When scissors attempt to cut the fabric, the hard fibres will tend to align with the axis of shear, forcing the blades apart, and therefore reducing the effectiveness of the scissors.
The fabric as described has a minor effect on rips - the viscous material may dissipate some of the energy associated with the frontier of the rip.