The most common and most likely answer to this crossword clue is the 4 plus 3 letter word DEEP SIX
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Buddy explains!
The straight part
We know that "to get rid of American" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to get rid of american = deep six.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 DEEP SIX mean?
DEEP SIX verb- To discard, get rid of, or cancel; to completely put an end to something.