"worthless sponging idler," 1863, American English slang, perhaps originally Civil War slang, from dead (adj.) + beat. Earlier dead beat was used colloquially as an adjectival expression, "completely beaten, so exhausted as to be incapable of further exertion" (1821), and perhaps the base notion is of "worn out, good for nothing." It is noted in a British source from 1861 as a term for "a pensioner." The English, characteristically, turned up their noses at the American use.
In England "dead beat" means worn out, used up. ... But here, "dead beat" is used, as a substantive, to mean a scoundrel, a shiftless, swindling vagabond. We hear it said that such a man is a beat or a dead beat. The phrase thus used is not even good slang. It is neither humorous nor descriptive. There is not in it even a perversion of the sense of the words of which it is composed. Its origin is quite beyond conjecture. ["Americanisms," in "The Galaxy," January 1878]
It also was used of a kind of regulating mechanism in pendulum clocks.