The most common and most likely answer to this crossword clue is the 4 plus 4 letter word SHUT DOWN
I've seen this crossword clue in The Daily Telegraph
S
H
U
T
D
O
W
N
More clues leading to the result SHUT DOWN
Buddy explains!

The straight part
We know that "Switch off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case switch off = shut down.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.