The most common and most likely answer to this crossword clue is the 5 plus 4 letter word SWEEP AWAY
I've seen this crossword clue in Financial Times
S
W
E
E
P
A
W
A
Y
Buddy explains!
The straight part
We know that "Swiftly and suddenly remove" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case swiftly and suddenly remove = sweep away.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.