The Greek root you are likely thinking of is "tom-" or "tem-" which does mean "cut" or "divide".
Here are some examples of words with this root:
* Anatomy: The study of the structure of living organisms.
* Atom: The smallest unit of an element.
* Dichotomy: A division into two parts.
* Epitome: A perfect example.
* Section: A part of something.
Let me know if you have any other Greek root questions!