Tick caught by mite cut in half (6)
I believe the answer is:
bisect
'cut in half' is the definition.
(synonyms)
'tick caught by mite' is the wordplay.
'tick' becomes 'sec' (I've seen this in another clue).
'caught by' is an insertion indicator.
'mite' becomes 'bit' (both can mean a small amount).
'sec' put inside 'bit' is 'BISECT'.
(Other definitions for bisect that I've seen before include "cross" , "Halve (angle)" , "Cut in half" , "Cut twenty [IN TWO]" , "Divide in half" .)