Comma
late 16th century (originally as a term in rhetoric denoting a group of words shorter than a colon; see colon1): via Latin from Greek komma ‘piece cut off, short clause’, from koptein ‘cut’.
wiktionary
From Latin comma, from Ancient Greek κόμμα(kómma), from κόπτω(kóptō, “I cut”)
etymonline
comma (n.)
punctuation mark, 1520s as a Latin word, nativized by 1590s, from Latin comma "short phrase or clause of a sentence or line of poetry," from Greek komma "clause in a sentence," also ""stamp, coinage," literally "piece which is cut off," from koptein "to strike, smite, cut off; disable, tire out," which is perhaps from PIE root *kop- "to beat, strike, smite" (see hatchet (n.)), or perhaps Pre-Greek.
Like colon (n.1) and period it was originally a Greek rhetorical term for a part of a sentence, and like them it has been transferred to the punctuation mark that identifies it. In reading aloud the punctuation mark is used to admit small interruptions in continuity of speech for the sake of clarity, but its purpose is to indicate grammatical structure.
