Vulgar puritan is beheaded (4)
I believe the answer is:
rude
'vulgar' is the definition.
(thesaurus)
'puritan is beheaded' is the wordplay.
'puritan' becomes 'prude' ('prude' can be a synonym of 'puritan').
'is beheaded' means to remove the first letter.
'prude' with its initial letter taken away is 'RUDE'.
(Other definitions for rude that I've seen before include "Impolite; unpolished" , "having no manners?" , "Uncultivated" , "Ill-mannered and coarse" , "Unmannerly" .)