The story
Originally from reference to a prank played on country bumpkins, in which they were encouraged to show their strength by whipping a cat that was harnessed to a load that was too heavy for it. This led to the sense of attempting to get more than can be provided, and by extension, to practice extreme parsimony. From there, it possibly evolved to the other senses, which tend to reflect the connotations of poverty and/or uselessness.
Etymology from Wiktionary, CC BY-SA 4.0.