The most common and most likely answer to this crossword clue is the 5 plus 2 plus 4 letter word TIRED OF LIFE
I've seen this crossword clue in The Guardian
T
I
R
E
D
O
F
L
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F
E
Buddy explains!
The straight part
We know that "Mentally resigned to go west" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mentally resigned to go west = tired of life.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.