The most common and most likely answer to this crossword clue is the 4 plus 7 letter word SPUD BASHING
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Buddy explains!
The straight part
We know that "Military punishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case military punishment = spud bashing.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 SPUD BASHING mean?
SPUD BASHING noun- The chore of peeling potatoes, especially when given as a punishment.