Other metabolic reactions aside, what causes beta oxidation to stop? To my understanding beta oxidation is when a fatty acid has its carbons plucked off in groups of 2 (acetyl groups) into acetly-coa which we can dump into the TCA. 

At what point would this process stop ? lets say we have a short chain fatty acid like butanoate (4c) would it still transfer an acetyl group leaving an acetate molecule ?
Different enzymes specialize to work on different size ranges. If the fatty acid is too short, it might not bind to enzymes that work on large fatty acids. An enzyme capable of binding short fatty acids might have most binding determinants targeting the CoA moiety instead of the fatty acid itself.


  At what point would this process stop ? lets say we have a short chain fatty acid like butanoate (4c) would it still transfer an acetyl group leaving an acetate molecule ?


It goes all the way as long as the CoA is attached.