c. 1300, "to make, with an edged tool or instrument, an incision in; make incisions for the purpose of dividing into two or more parts; remove by means of a cutting instrument;" of an implement, "have a cutting edge," according to Middle English Compendium from a presumed Old English *cyttan, "since ME has the normal regional variants of the vowel." Others suggest a possible Scandinavian etymology from North Germanic *kut- (source also of Swedish dialectal kuta "to cut," kuta "knife," Old Norse kuti "knife"), or that it is from Old French couteau "knife."
From early 14c. as "to make or fashion by cutting or carving." From c. 1400 as "to intersect or cross." From early 15c. as "abridge or shorten by omitting a part."
Meaning "to wound the sensibilities of" is from 1580s (to cut the heart in the same sense is attested from early 14c.). Sense of "sever connection or relations with" is from 1630s.
Meaning "to be absent without excuse" is British university slang from 1794. Colloquial or slang sense of "move off with directness and rapidity" is from 1580s. Meaning "divide (a deck of cards) at random into parts before the deal" to prevent cheating is from 1530s.
Meaning "to dilute, adulterate" (liquor, etc.) is by 1930. Colloquial sense of "to divide or share" is by 1928, perhaps an image from meat-carving at table. As a director's call to halt recording or performing, by 1931 (in an article about Pete, the bulldog with the black-ringed eye in the Hal Roach studios shorts, who was said to know the word). The sense of "perform, execute" (c. 1600) is in cut capers "frisk about;" cut a dash "make a display."
To cut down is from late 14c. as "to fell;" by 1821 as "to slay" (as with a sword); 1857 as "to curtail." 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.
To cut in "enter suddenly and unceremoniously" is from 1610s; sense of "suddenly join in conversation, interrupt" is by 1830. To cut up "cut in pieces" is from 1570s. To cut back is from 1871 as "prune by cutting off shoots," 1913 in cinematography, "return to a previous scene by repeating a part of it," 1943 as "reduce, decrease" (of expenditures, etc.). To cut (something) short "abridge, curtail, interrupt" is from 1540s.
In nautical use to cut a feather (1620s) is to move so fast as to make water foam under the bow. To cut and run (1704) also is originally nautical, "cut cable and set sail immediately," as in an emergency, hence, generally, "to make off suddenly."
To cut the teeth "have the teeth grow through the gums" as an infant is from 1670s. To cut both ways in the figurative sense of "have a good and bad effect" is from c. 1600. To cut loose "set (something) free" is by 1828; intransitive sense "begin to act freely" is by 1909.
Cut it out "remove (something) by or as if by cutting" yielded a figurative use in the command cut it out! "Stop! That's enough!" by 1933. The evolution seems to have begun earlier. A piece attributed to the Chicago Live Stock World that made the rounds in trade publications 1901-02 begins:
When you get 'hot' about something and vow you are going to rip something or somebody up the back—cut it out.
If you feel disposed to try the plan of building yourself up by tearing some one else down—cut it out.
Playing on both senses, it ends with "Should you, after reading this preachy stuff, fear you might forget some of the good advice—cut it out."