The most common and most likely answer to this crossword clue is the 4 letter word FUME
I've seen this crossword clue in The Guardian
F
U
M
E
More clues leading to the result FUME
Buddy explains!

The straight part
We know that "Blow up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case blow up = fume.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FUME mean?
FUME noun- A gas or vapour/vapor that is strong-smelling or dangerous to inhale.
- A material that has been vaporized from the solid or liquid state to the gas state and re-coalesced to the solid state.
- Rage or excitement which deprives the mind of self-control.
- Anything unsubstantial or airy; idle conceit; vain imagination.
- The incense of praise; inordinate flattery.
- A passionate person.
- To expose (something) to fumes; specifically, to expose wood, etc., to ammonia in order to produce dark tints.
- To apply or offer incense to.
- To emit fumes.
- To pass off in fumes or vapours.
- To express or feel great anger.
- To be as in a mist; to be dulled and stupefied.