The most common and most likely answer to this crossword clue is the 6 plus 9 letter word PENCIL SHARPENER
I've seen this crossword clue in Financial Times
P
E
N
C
I
L
S
H
A
R
P
E
N
E
R
More clues leading to the result PENCIL SHARPENER
- With which writer discovers new lead?
- Writer’s device for emphasising point?
- It helps writer to come to the point
- It gives more point to your writing
- With which writer makes good points?
- What might make the point for a writer?
- Article used by writer to make a point
- Device used by writer to make a point
- It’s used to make a point by a writer keen to back Descartes
- What one may resort to when there’s no point in solving
Buddy explains!

The straight part
We know that "I make a point by removing dead wood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i make a point by removing dead wood = pencil sharpener.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.