Why the use of 'clock' in the following sentence?

To clock someone indeed has something to do with a clock: a clock has a face. To clock (verb):

Brit and Austral and NZ: to strike, esp on the face or head; to strike sharply or heavily: clocked him in the face.

It's birth is somewhat roundabout, however. Initially, the phrase using clock to connote violence was "to clean someone's clock":

To beat or defeat decisively: "Immense linemen declared their intentions to clean the clocks of opposing players" (Russell Baker).

According to Cassells Dictionary of Slang:

TO CLEAN SOMEONE’S CLOCK, phrase [1940’s and still in use] (originated in U.S.) 1) to beat up severely. 2) to take all someone’s money, especially during gambling (cf. ‘clean out’). [figurative use of Standard English]; ? link to US railroad jargon ‘clean the clock,’ to apply the airbrakes and thus bring the train to a sudden stop. The ‘clock’ in question is the air gauge, which on halting, immediately registers zero and is thus ‘clean.’].

Yet in Great Britain:

"To clean" gained a sense of "to clean out" in 1812, applied to victims of thieves or gamblers. In a few years, a slang meaning of clean became "to drub, defeat, wipe out." - Wm. Safire, NYT

In 1904, O. Henry wrote in a story: "I recon we'll fix your clock for a while."

Thus was developed to clean (defeat, thrash, trounce) one's clock (face, head, person). Earliest citation so far: in 1959, the novelist Sam Cochrell wrote this dialogue: "Don't give me that guff. You're not a corporal anymore." "I don't have to be a corporal to clean your clock." - Wm. Safire, NYT

It's about violence, but "clock you" has tangled history.

clock (verb):

The slang sense of "hit, sock" is 1941, originally Australian, probably from earlier slang clock (n.) "face" (1923). Related: Clocked; clocking.

to clock:

The act of hitting a person: Try to steal my AMG, I'll clock you.

Also see: clocked

To completly smash a video game. Meaning you get perfect scores and without losing a single life. Holy shit Billy Mitchell clocked pac man.

With regard to "clean [one's] clock," I was surprised to find a British instance of this phrase from the nineteenth century. From Peter Henry Emerson, Birds, Beasts and Fishes of the Norfolk Broadland (1895), a hunter describes a heron he has jut shot:

I know 'em [herons], sir, better than most folk. I hev kept several tame ones—young birds they were. One I had ate suet, a wiper nigh 20 inches long; while I had a young one ate a roach [a kind of fish] weighing fifteen ounces, eels all you like up to half a pound, frogs, mice, stanacles, and dead birds. They like they're own sort best; they are death on birds. I do a bit of stuffing, and as sure as I get gutting a bird, in comes my nabs and steals some. They're a bird wonderful quick of hearing, wonderful quick-sighted, and wonderful quick to digest their food—that runs through them like water." He paused as he poured his shot into his rough musket, but resumed —

"Old Frank [the heron the man shot] ha' done me out of many an eel—the warmint—but I ha' cleaned his clock now, and I shall get tree bob for him. I only wish he was that white 'un what I be after one day last summer, nigh up to arter harvest; but he was too quick for pill-garlic."

This instance is also cited in Joseph Wright's English Dialect Dictionary, which defines "to clean a person's clock" as meaning "to 'do' for him."

The next Google Books search match is from John Arthur Nelson, The New Disciple: A Story of Big Business and a High Ideal (1921), a book published in New York:

Mike staggered steps under the unexpected impetus. He turned and braced himself in a belligerent attitude, and cried:

"Come on, you dirty stool-pigeon. I'd just as soon begin on you as anybody."

"Atta boy, Mike!"..."Stand up to him!"..."Clean his clock!"..."We'll see that you get 'fair play!" came from all parts of the crowd. It was plain to see where all the sympathy lay.

The next match (and the last before 1941) appears in a letter from Sylvania, Ohio, in the the April 1922 issue of Hunter Trader—Trapper magazine:

I saw a better fight when we reached the house. The women were up, pard's wife cleaned his clock because he did not get back at midnight as they had a lot of chores to do, and cows to milk. She would not let him stay for breakfast so they started for home. That was the last time he got over to take a hunt with me.

Of these three metaphorical occurrences of "clean [one's] clock," only the second seems to mean "hit [someone] in the face." Though it's hard to say which country or region deserves credit for the origin of the phrase, the first Google Books examples of it are from England—and it was in use in both England and the United States long before the 1940s.