A razor cut? The devil it is! (4)

I believe the answer is:

nick

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'a razor cut?' is the definition.
'nick' can be an answer for 'cut?' (nick is a kind of cut). I am not sure about the 'a razor' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for nick that I've seen before include "Small cut - if old, the devil" , "Steal (informal)" , "Slammer - swipe" , "Filch" , "Minor injury" .)

I've seen this clue in The Irish Independent.

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