Animal one cuts horn off (5)
I believe the answer is:
rhino
'animal' is the definition.
(short for rhinoceros)
'one cuts horn off' is the wordplay.
'one' becomes 'i' (Roman numeral).
'cuts' means one lot of letters goes inside another (some letters cut their way into a word).
'off' is an anagram indicator.
'horn' is an anagram of 'rhno'.
'i' placed within 'rhno' is 'RHINO'.
(Other definitions for rhino that I've seen before include "Horned jungle beast" , "Stumpy" , "Horned pachyderm" , "Hi, Ron! (anag)" , "One charging" .)