One third of American state is cut off, unfortunately (4)
I believe the answer is:
alas
'unfortunately' is the definition.
('alas' is used to express regret)
'one third of american state is cut' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'third of american' becomes 's' (I can't explain this - if you can you should believe this answer much more).
'state' becomes 'LA' (abbreviation for Louisiana).
'is cut' indicates putting letters inside (some letters have cut into others).
'a'+'s'='as'
'as' going around 'la' is 'ALAS'.
'off' is the link.
Can you help me to learn more?
(Other definitions for alas that I've seen before include "Proper, respectable" , "Sad to say!" , "I'm sorry to say" , "woebegone expression" , "Archaic exclamation of sorrow or regret" .)