Slight adjustment of width at first cutting wood (5)
I believe the answer is:
tweak
'slight adjustment' is the definition.
(I've seen this before)
'width at first cutting wood' is the wordplay.
'at first' indicates taking the first letters.
'cutting' indicates putting letters inside (some letters cut their way into a word).
'wood' becomes 'teak' (type of timber).
The first letter of 'width' is 'w'.
'w' inserted into 'teak' is 'TWEAK'.
'of' acts as a link.
(Other definitions for tweak that I've seen before include "Pinch sharply" , "spin, thus?" , "Make minor adjustment" , "Edit" , "Fine adjustment (colloq.)" .)