From my limited testing, it appears that the Kindle app for Mac will include the citation as the last line of whatever you copy from it, preceded by a blank line.
So the question becomes: “How do we delete the last line from something?”
The answer (well, an answer) is
which will delete the last line of a file, or of the input which is given to it.
That will leave you with a blank line at the end of your pasted text. If you want to delete that line too, you can use
sed '$d' again, like so:
sed '$d' | sed '$d'
Assuming that will receive the pasteboard from
stdin and send the result to
stdout that should work.
I haven’t used Automator much, but it would be easy to do this in Keyboard Maestro.