Middle English kerven (the initial -k- is from influence of Scandinavian forms), from Old English ceorfan (class III strong verb; past tense cearf, past participle corfen) "to cut," also "cut down, slay; cut out," from West Germanic *kerbanan (source also of Old Frisian kerva, Middle Dutch and Dutch kerven, German kerben "to cut, notch"), from PIE root *gerbh- "to scratch," making carve the English cognate of Greek graphein "to write," originally "to scratch" on clay tablets with a stylus.
Once extensively used and the general verb for "to cut;" most senses now have passed to cut (v.) and since 16c.
carve has been restricted to specialized senses such as "cut (solid material) into the representation of an object or a design" (late Old English); "cut (meat, etc.) into pieces or slices" (early 13c.); "produce by cutting" (mid-13c.); "decorate by carving" (late 14c.). Related: Carved; carving. The original strong conjugation has been abandoned, but archaic past-participle adjective carven lingers poetically.
"craftsman whose occupation is the making of knives and other cutting instruments," c. 1400 (c. 1200 as a surname), from Anglo-French cuteler, Old French coutelier (12c., Modern French coutelier) "knife-maker," from Latin cultellarius, from cultellus "small knife," diminutive of culter "knife, plowshare," from PIE *kel-tro-, suffixed form of root *skel- (1) "to cut."
"to make a cut," 1540s, from French inciser (15c.), from Old French enciser "cut, cut out, slice" (12c.), from Latin incisus, past participle of incīdere "to cut into, cut open, engrave," from in- "into, in, on, upon" (from PIE root *en "in") + -cidere, combining form of caedere "to cut" (from PIE root *kae-id- "to strike"). In geology, of rivers, from 1893. Related: Incised; incising.
"cut off or away, pare off," 1650s, from Latin resectus, past participle of resecare "to cut off, cut loose, curtail," from re-, here perhaps an intensive prefix (see re-), + secare "to cut" (from PIE root *sek- "to cut"). The surgical sense of "excising of some part," of a bone, etc., (1846) seems to be the sole surviving one. Related: Resected; resecting.
"capable of being cut or divided," 1620s, from Latin scissilis, from scindere "to cut" (from PIE root *skei- "to cut, split").