The most common and most likely answer to this crossword clue is the 8 letter word DEMEANED
I've seen this crossword clue in Independent
D
E
M
E
A
N
E
D
Buddy explains!

The straight part
We know that "Put down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put down = demeaned.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 DEMEANED mean?
DEMEANED verb- To debase; to lower; to degrade.
- To humble, humble oneself; to humiliate.
- To mortify.
- To manage; to conduct; to treat.
- (now rare) To conduct; to behave; to comport; followed by the reflexive pronoun.
- To subtract the mean from (a value, or every observation in a dataset).