With an exclamation of annoyance, blow up (5)
I believe the answer is:
blast
'blow up' is the definition.
(thesaurus)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for blast that I've seen before include "Great time: explosion" , "Blow up or swear" , "Sudden, strong current of air" , "Explosion - mild oath" , "Loud horn sound" .)