Supervised and completed cut (7)
I believe the answer is:
oversaw
'supervised' is the definition.
('oversee' can be a synonym of 'supervise')
'completed cut' is the wordplay.
'completed' becomes 'over' ('over' can be a synonym of 'completed').
'cut' becomes 'saw' (sawing is a kind of cutting).
'over'+'saw'='OVERSAW'
'and' is the link.
(Other definitions for oversaw that I've seen before include "Supervised" , "What supervisor did" , "Managed" , "watcher" .)