Badly mix clue, go off to part of the Atlantic (4,2,6)
I believe the answer is:
gulf of mexico
'to part of the atlantic' is the definition.
('Gulf of Mexico' is part of 'atlantic')
'badly mix clue go off' is the wordplay.
'badly' indicates an anagram.
'mix'+'clue'+'go'+'off'='mixcluegooff'
'mixcluegooff' is an anagram of 'GULF OF MEXICO'.
(Other definitions for gulf of mexico that I've seen before include "Area of hurricanes and oil leaks" , "Sea south of Texas" , "Arm of the Atlantic to the south of the United States" .)