The most common and most likely answer to this crossword clue is the 6 plus 6 letter word DUMDUM BULLET
I've seen this crossword clue in Financial Times
D
U
M
D
U
M
B
U
L
L
E
T
Buddy explains!
The straight part
We know that "Exploding slug" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exploding slug = dumdum bullet.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.