Cut dead awkward Luddite ignoring theologian (6)
I believe the answer is:
dilute
'cut' is the definition.
('dilute' can be a synonym of 'cut')
'dead awkward luddite ignoring theologian' is the wordplay.
'dead' becomes 'd'.
'awkward' indicates an anagram.
'ignoring' indicates named letters should be taken away.
'theologian' becomes 'dd' (Doctor of Divinity degree).
'luddite' with 'dd' removed is 'luite'.
'luite' anagrammed gives 'ilute'.
'd'+'ilute'='DILUTE'
(Other definitions for dilute that I've seen before include "having less concentration" , "not neat" , "Make (a liquid) thinner" , "Reduce concentration of a liquid" , "Thin out, make less strong" .)