The most common and most likely answer to this crossword clue is the 11 letter word UNDERMINING
I've seen this crossword clue in The Times
U
N
D
E
R
M
I
N
I
N
G
Buddy explains!

The straight part
We know that "Damaging" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case damaging = undermining.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 UNDERMINING mean?
UNDERMINING verb- To dig underneath (something), to make a passage for destructive or military purposes; to sap.
- To weaken or work against; to hinder, sabotage.
- To erode the base or foundation of something, e.g. by the action of water.
- The act or process by which something is undermined.