I am wondering how the phrase "to cut someone down to size" came to mean what it does. I'm not sure if it is true but I read somewhere that the origin of the phrase goes back to the Middle English story of King Arthur cutting off a giant's legs at the knees. Also, I don't know how common the phrase is in American English.
The idiomatic expression does not appear to be as old as Middle Ages.
According to Etymonline it is the figurative usage of the literal one:
To cut (someone or something) down to size is from 1821 as "reduce to suitable dimensions;" the figurative sense, "reduce to the proper level of importance," is by 1927.
From The American Secretaries of State and Their Diplomacy, Volume 11 - Samuel Flagg Bemis. 1927
Wood wished to cut him down to size. Ainsworth knew it, and chose as a time for rebellion the moment when Wood and Stimson sought to abolish the bimonthly muster roll.....
According to GDoS it is of black AmE origin:
cut someone down (v.):
(orig. US black) to challenge, with the intention of proving one’s superiority, usu. in the context of verbal, dancing or musical competitions.
1946 [US] Mezzrow & Wolfe Really the Blues 231: All the contenders for the title [...] wanted to cut him down – that is, prove they were the best in the field.
1954 [US] Hepster’s Dict. 2: Cut you down – Put somebody in place.
1968 [US] G. Cuomo Among Thieves 216: It was to your benefit that someone like Penney tried to fag you early, as long as you could cut him down. The word got around, and people left you alone.
1994 [US] N. McCall Makes Me Wanna Holler (1995) 329: They cut her down without batting an eye.
The origin can be as old as the Ancient Greek mythology which has a similar story, of the Bed of Procrustes. Procrustes (Greek: Προκρούστης Prokroustes, "the stretcher [who hammers out the metal]") was a rogue smith and bandit from Attica who attacked people by stretching them or cutting off their legs, so as to force them to fit the size of an iron bed.
The word "Procrustean" is thus used to describe situations where different lengths or sizes or properties are fitted to an arbitrary standard.