haircut (n.)

mid-15c., "a certain length" of something; 1520s, "gash, incision, opening made by an edged instrument," from cut (v.).

Meaning "piece cut off" (especially of meat) is from 1590s. Figurative sense of "a wounding sarcasm" is from 1560s. Meaning "an excision or omission of a part" is from c. 1600. Sense of "a reduction" is by 1881. Meaning "manner in which a thing is cut" is from 1570s, hence "fashion, style, make" (1580s).

Dialectal or local sense of "a creek or inlet" is from 1620s. Meaning "channel or trench made by cutting or digging" is from 1730. Meaning "block or stamp on which a picture is engraved" is from 1640s. Sense of "act of cutting a deck of cards" is from 1590s. Cinematic sense of "a quick transition from one shot to the next" is by 1933. Meaning "share" (of profit, loot, etc.) is by 1918.

Meaning "phonograph recording" is by 1949; the verb in the sense "make a recording" is by 1937, from the literal sense in reference to the mechanical process of making sound recordings.

Instead of a cutting tool actually operated by the sound vibrations from the voices or instruments of performing artists, the panatrope records are cut by a tool that is operated electrically. ["The New Electric Phonograph," in Popular Science, February 1926]. 

A cut above "a degree better than" is from 1818. Cold-cuts "cooked meats sliced and served cold" (1945) translates German kalter Aufschnitt.

Old English hær "hair, a hair," from Proto-Germanic *hēran (source also of Old Saxon, Old Norse, Old High German har, Old Frisian her, Dutch and German haar "hair"), perhaps from PIE *ghers- "to stand out, to bristle, rise to a point" (source also of Lithuanian šerys "bristle;" see horror).

Spelling influenced by Old Norse har and Old English haire "haircloth," from Old French haire, from Frankish *harja or some other Germanic source (see above). Hair-dye is from 1803. To let one's hair down "become familiar" is first recorded 1850. Homeopathic phrase hair of the dog (that bit you), remedy from the same thing that caused the malady, especially a drink on the morning after a debauch, 1540s in English, is in Pliny.