The most common and most likely answer to this crossword clue is the 6 plus 4 letter word THUMBS DOWN
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More clues leading to the result THUMBS DOWN
Buddy explains!

The straight part
We know that "They mean no" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they mean no = thumbs down.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 THUMBS DOWN mean?
THUMBS DOWN noun- A gesture signifying disapproval; a thumb pointing down out of a fist.
- A rejection or refusal.
- To disapprove with a thumbs-down sign.