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detail (n.): c. 1600, from French détail, from Old French detail "small piece or quantity," literally "a cutting in pieces," from detaillier "cut in pieces," from de- "entirely" (see de-) + taillier "to cut in pieces" (see tailor).

Modern sense is from French en détail "piece by piece, item by item" (as opposed to en gros), a commercial term used where we would today use retail. Military sense is 1708, from notion of "distribution in detail of the daily orders first given in general," including assignment of specific duties.
dichotomy (n.): c. 1600, from Greek dichotomia "a cutting in half," from dicha "in two, asunder" (related to dis "twice") + temnein "to cut" (see tome).
incision (n.): late 14c., "a cutting made in surgery," from Old French incision (13c.) and directly from Latin incisionem (nominative incisio) "a cutting into," noun of action from past participle stem of incidere "to cut in," from in- "into, in, on, upon" (see in- (2)) + -cidere, comb. form of caedere "to cut" (see -cide). Meaning "act of cutting into" is from early 15c.
scissors (n.): late 14c., sisoures, from Old French cisoires (plural) "shears," from Vulgar Latin *cisoria (plural) "cutting instrument," from *cisus (in compounds such as Latin excisus, past participle of excidere "to cut out"), ultimately from Latin caedere "to cut" (see -cide). Spelling with sc- is 16c., from influence of Medieval Latin scissor "tailor," in classical Latin "carver, cutter," from past participle stem of scindere "to split."

Usually with pair of (attested from c. 1400) when indication of just one is required, but a singular form without the -s occasionally was used (cysowre, mid-15c.). In Scotland, shears answers for all sizes, according to OED; but in England generally that word is used only for those too large to be worked by one hand. Sense in wrestling is from 1904. Oh scissors! was a 19c. exclamation of impatience or disgust (1843). In reference to a type of swimming kick, from 1902 (the image itself is from 1880s).
segmentation (n.): 1650s, "a cutting in small pieces;" 1851 of cells, from segment (v.) + -ation.
arteriotomy: "The operation of cutting into or opening an artery (in early use especially for the purpose of bloodletting); an instance of this", Mid 17th cent.; earliest use found in Thomas Johnson (d. 1644), apothecary and soldier. From Middle French, French artériotomie and its etymon post-classical Latin arteriotomia operation of cutting into an artery from Hellenistic Greek ἀρτηριοτομία from ἀρτηριο- + ancient Greek -τομία.