To begin at the beginning, "clock" has been slang for the human face since the mid-nineteenth century, based on its supposed resemblance to the face of a clock. "Clock" as a verb has also been slang for "to punch in the face or strike violently" since the early 20th century, again based on the clock-face metaphor.

Elsewhere in the world of fisticuffs, according to the Random House Historical Dictionary of American Slang, "clean" has been slang for "vanquish" since the early 19th century. The Random House dictionary also lists "fix someone's clock" as a slang term for "to finish someone," first attributed to the writer O. Henry in 1908. Curiously, the first citation for the whole phrase "clean someone's clock" comes only in 1959, but we can assume it had been around for awhile before that.

Even with all this evidence tying faces and punches together, I must say that there is another possible source for "clean someone's clock." In railroad slang, an engineer who applies the train's air brakes in an emergency is said to "clean the clock" or "wipe the gauge" as the speedometer needle drops to zero. It seems logical that such a graphic metaphor would be the perfect way to describe stopping an opponent in his tracks, and even if this is not the source of the phrase, it may have contributed to its popularization.