"to thrust, push; jostle;" also, "prod, to drive (cattle, etc.) by poking and prodding," late 14c., from Old French ponchonner "to punch, prick, stamp," from ponchon "pointed tool, piercing weapon" (see punch (n.1)). Meaning "to pierce, emboss with a tool" is from early 15c.; meaning "to stab, puncture" is from mid-15c. To punch a ticket, etc., is from mid-15c. To punch the clock "record one's arrival at or departure from the workplace using an automated timing device" is from 1900. Related: Punched; punching.

Perhaps you are some great big chief, who has a lot to say.

Who lords it o'er the common herd who chance to come your way;

Well, here is where your arrogance gets a dreadful shock,

When you march up, like a private, salute, and PUNCH THE CLOCK.

[from "Punch the Clock," by "The Skipper," The Commercial Telegraphers' Journal, May 1912]

Specialized sense "to hit with the fist" first recorded 1520s. Compare Latin pugnare "to fight with the fists," from a root meaning "to pierce, sting." In English this was probably influenced by punish; "punch" or "punsch" for "punish" is found in documents from 14c.-15c.:

punchyth me, Lorde, and spare my blyssyd wyff Anne. [Coventry Mystery Plays, late 15c.]

To punch (someone) out "beat up" is from 1971.