Cut one out — no irritation (5)
I believe the answer is:
notch
'cut' is the definition.
(notch is a kind of cut)
'one out no irritation' is the wordplay.
'one' becomes 'i' (roman numeral).
'out' suggests deleting specific letters.
'irritation' becomes 'itch' (I've seen this before).
'no'+'itch'='noitch'
'noitch' with 'i' taken out is 'NOTCH'.
(Other definitions for notch that I've seen before include "Make the cut" , "Incision; indentation" , "V-shaped nick" , "Indentation, nick" , "Cleft" .)