Cryptic crossword clue
Low

The most common and most likely answer to this crossword clue is the 3 letter word MOO

I've seen this crossword clue in The Guardian
M
O
O


Buddy explains!

The straight part
We know that "state of mind on departure of daughter (3)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case state of mind on departure of daughter (3) = moo.
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 MOO mean?

MOO noun
  1. The characteristic lowing sound made by cattle.
  2. A foolish woman.
MOO verb
  1. Of a cow or bull, to make its characteristic lowing sound.
MOO interjection
  1. The characteristic sound made by a cow or bull.

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