Extremely cut off, a city goes under (8)
I believe the answer is:
severely
'extremely' is the definition.
(both can mean to a profound degree)
'cut off a city goes under' is the wordplay.
'cut off' becomes 'sever' (to sever is to cut).
'a city' becomes 'ely' (Ely is a city in Cambridgeshire).
'goes under' is a charade indicator (letters next to each other).
'sever'+'ely'='SEVERELY'
(Other definitions for severely that I've seen before include "With sternness" , "Harshly, gravely" , "In a stern manner" , "Sternly or gravely" , "Intensely; harshly" .)