Vexed utterance is a puzzle (9)
I believe the answer is:
crossword
'a puzzle' is the definition.
(type of puzzle)
'vexed utterance' is the wordplay.
'vexed' becomes 'cross' (both can mean angry).
'utterance' becomes 'word' (I've seen this in another clue).
'cross'+'word'='CROSSWORD'
'is' acts as a link.
(Other definitions for crossword that I've seen before include "this, appropriately" , "What's here" , "(Usually) black and white puzzle" , "Cruciverbal test" , "Puzzle like this one" .)