They cut bill dropped by flyers at sea (6)
I believe the answer is:
razors
'they cut' is the definition.
(razors cut hair)
'bill dropped by flyers at sea' is the wordplay.
'dropped by' suggests deleting specific letters.
'flyers at sea' becomes 'razorbills' (razorbills are seabirds).
'razorbills' with 'bill' taken away is 'RAZORS'.
(Other definitions for razors that I've seen before include "Shavers" , "Edge tools" , "Shaving instruments" , "Shaving items" , "Instruments with sharp blades" .)