Cuts off facial hair on edge, regularly (8)

'cuts' is the definition.
The answer and definition can be both to do with contact as well as being verbs in their -s form.
Maybe there's an association between them I don't understand?

'facial hair on edge regularly' is the wordplay.
'facial hair' becomes 'tache' (I've seen this before).
'on' means one lot of letters goes inside another.
'edge regularly' becomes 'des' (I can't explain this - if you can you should give a lot more credence to this answer).
'tache' going into 'des' is 'DETACHES'.

'off' is the link.

Can you help me to learn more?