Strip joint vulgar, first to go (6)

I believe the answer is:

denude

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'strip' is the definition.
(I know that strip can be written as denude)

'joint vulgar first to go' is the wordplay.
'joint' becomes 'den' (I can't justify this - if you can you should give a lot more credence to this answer).
'vulgar' becomes 'rude' (vulgar can mean rude or gross).
'first to go' means to remove the first letter.
'rude' with its initial letter taken off is 'ude'.
'den'+'ude'='DENUDE'

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(Other definitions for denude that I've seen before include "Lay bare" , "Strip, deprive, of" , "Strip - expose" , "Strip cover from, as leaves from trees" , "Uncover" .)

I've seen this clue in The Times.

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