Shoot me a beet?

[HaraKiriBlade]

What does it mean? (my shortest question ever!)

[Tdol]

And one of your hardest- the only references I can fid to it are from the very book you're reading. This text suggests it's a catchphrase that shows an influence of Thomas Pynchon, if that helps:
http://tarlton.law.utexas.edu/lpop/e...mccarron24.htm
In other words, it's a a nonsense phrase.