The most common and most likely answer to this crossword clue is the 5 letter word ADZES
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More clues leading to the result ADZES
Buddy explains!

The straight part
We know that "Cutters of wood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cutters of wood = adzes.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 ADZES mean?
ADZES noun- A cutting tool that has a curved blade set at a right angle to the handle and is used in shaping wood.
- To shape a material using an adze.