Groove (3)
'groove' is the definition.
(I know that groove is a more specific form of the action incise)
This is all the clue.
(Other definitions for cut that I've seen before include "Sever; ignore" , "A share of the profits" , "Axe" , "Shorten; (one's) share" , "dropped" .)
'groove' is the definition.
(I know that groove can be written as rut)
This is the entire clue.
(Other definitions for rut that I've seen before include "Oestrus" , "Groove made by wheels" , "Groove made by wheel" , "Boring groove to be stuck in!" , "A deep track - get out of it" .)
(Other definitions for dance that I've seen before include "Move(ment) to music" , "spin?" , "Measure" , "Fling" , "Terpsichorean activity" .)