A wound produced by a point that's sharp (5)
I believe the answer is:
acute
'sharp' is the definition.
('acute' can be a synonym of 'sharp')
'a wound produced by a point' is the wordplay.
'a wound' becomes 'cut' (cut is a kind of wound**).
'produced by' says to put letters next to each other.
'point' becomes 'e' (E is an example).
'cut' put after 'a' is 'acut'.
'acut'+'e'='ACUTE'
'that's' acts as a link.
(Other definitions for acute that I've seen before include "Sharp or crucial" , "Shrewd; serious" , "Sharp; severe" , "Sharp like angle" , "Severe; French accent" .)