Split wood: remove to the periphery (4,3)

I believe the answer is:

dash off

'split' is the definition.
(both can mean to leave)

'wood remove to the periphery' is the wordplay.
'wood' becomes 'ash' (ash is a kind of wood).
'remove' becomes 'doff' (I've seen this before).
'to the periphery' means one lot of letters goes inside another (outside letters go round the periphery).
'ash' placed into 'doff' is 'DASH OFF'.

(Another definition for dash off that I've seen is " Rush away".)

I've seen this clue in The Times.

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