The most common and most likely answer to this crossword clue is the 4 letter word DARN
I've seen this crossword clue in The Daily Telegraph
D
A
R
N
More clues leading to the result DARN
Buddy explains!

The straight part
We know that "Mild expletive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mild expletive = darn.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 DARN mean?
DARN verb- Euphemism of damn.
- Damn.
- (degree) Damned.
- Damn.
- A place mended by darning.
- To repair by stitching with thread or yarn, particularly by using a needle to construct a weave across a damaged area of fabric.