The most common and most likely answer to this crossword clue is the 5 letter word WHISK
I've seen this crossword clue in The Daily Telegraph
W
H
I
S
K
More clues leading to the result WHISK
Buddy explains!

The straight part
We know that "Vigorously mix" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vigorously mix = whisk.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 WHISK mean?
WHISK noun- A quick, light sweeping motion.
- A kitchen utensil, made from stiff wire loops fixed to a handle, used for whipping (or a mechanical device with the same function).
- A bunch of twigs or hair etc, used as a brush.
- A small handheld broom with a small (or no) handle.
- A plane used by coopers for evening chines.
- A kind of cape, forming part of a woman's dress.
- An impertinent fellow.
- To move something with quick light sweeping motions.
- In cooking, to whip e.g. eggs or cream.
- To move something rapidly and with no warning.
- To move lightly and nimbly.
- The card game whist.