In comic making, what purpose does cutting a single image into panels serve?
The division in panels is used to signify the passing of time, occurring in the direction of reading. This is known as sequential narrative. Whether the panels consist of different images or divide what appears to be a single image, does not matter for this interpretation.
Often when it concerns a single image, this division is combined with text - be it dialogue, description, or thoughts of the person(s) depicted. It can symbolize a lack of physical or emotional change, a stability, solidification, or unyieldingness:

Chris Samnee. Daredevil, issue #25, 2011