c. 1300 (mid-12c. in surnames), "small axe with a short handle," designed to be used by one hand, from Old French hachete "small combat-axe, hatchet," diminutive of hache "axe, battle-axe, pickaxe," possibly from Frankish *happja or some other Germanic source, from Proto-Germanic *hapjo- (source also of Old High German happa "sickle, scythe").
This is perhaps from PIE root *kop- "to beat, strike" (source also of Greek kopis "knife," koptein "to strike, smite," komma "piece cut off;" Lithuanian kaplys "hatchet," kapti, kapiu "to hew, fell;" Old Church Slavonic skopiti "castrate," Russian kopat' "to hack, hew, dig;" Albanian kep "to hew").
Hatchet-face in reference to one with sharp and prominent features is from 1650s. In Middle English, hatch itself was used in a sense "battle-axe." In 14c., hang up (one's) hatchet meant "stop what one is doing." Phrase bury the hatchet "lay aside instruments of war, forget injuries and make peace" (1754) is from a Native American peacemaking custom described from 1680. Hatchet-man was originally California slang for "hired Chinese assassin" (1880), later extended figuratively to journalists who attacked the reputation of a public figure (1944).