The most common and most likely answer to this crossword clue is the 8 letter word EXCLAVES
I've seen this crossword clue in The Guardian
E
X
C
L
A
V
E
S
Buddy explains!

The straight part
We know that "cut off areas of country" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut off areas of country = exclaves.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EXCLAVES mean?
EXCLAVES noun- A portion of a country's territory not connected to the main part
- A detached part of an organ, as of the pancreas, thyroid, or other gland.