Give a slight cut (6)
I believe the answer is:
ignore
'cut' is the definition.
(cut can mean to ignore socially)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for ignore that I've seen before include "Refuse to notice or acknowledge" , "Intentionally disregard" , "Region (anag)" , "Disregard - cut" , "Deliberately overlook" .)