If you cut off contact with certain people, you ostracise them.
If you cut yourself off from contact by all others, you live as a recluse or seclude yourself.
isolate or seclude
The word that means cut into two parts is bisect. The root of the word comes from "bi" meaning two and "secare" meaning to cut.
"Bisect" is a word that means cut into two halves which starts with bi.
The word "isolation" originates from the Latin word "insula," which means island. This reflects the idea of being separated or cut off from others, similar to an island being alone in the sea.
I don't think unsular is a word. Insular, though, means isolated, inaccessible, cut off, closed, separate, segregated, detached, not wanting contact with others. The word comes from the meaning of an island.
rut
Bisect.
slice
slash
valley
Division means to divide or cut into parts or pieces.Division means to divide or cut into parts or pieces.
"Inter-" is the prefix and it means "between" or "among." The root word is "sect," which means "to cut" or "to divide." Together, they form the word "intersect," which means to cut or divide between two things.