Cuts the hairs so oddly (5)
I believe the answer is:
tears
'cuts' is the definition.
'the hairs so oddly' is the wordplay.
'oddly' means one should take alternating letters.
'the'+'hairs'+'so'='thehairsso'
The alternating letters of 'thehairsso' are 'TEARS'.
(Other definitions for tears that I've seen before include "Shed them and cry" , "Moves very quickly" , "emotional reaction!" , "Lacerations (before bedtime?)" , "Rush special" .)