"to hit, strike, beat," mid-12c., from Old English smitan, which however is attested only as "to daub, smear on; soil, pollute, blemish, defile" (strong verb, past tense smat, past participle smiten), from Proto-Germanic *smitan (cf. Swedish smita, Danish smide "to smear, fling," Old Frisian smita, Middle Low German and Middle Dutch smiten "to cast, fling," Dutch smijten "to throw," Old High German smizan "to rub, strike," German schmeißen "to cast, fling," Gothic bismeitan "to spread, smear"). "The development of the various senses is not quite clear, but that of throwing is perh. the original one" [OED]. Watkins suggests "the semantic channel may have been slapping mud on walls in wattle and daub construction" and connects it with PIE *sme- "to smear;" Klein's sources also say this.
Sense of "slay in combat" (c.1300) is from Biblical expression smite to death, first attested c.1200. Meaning "visit disastrously" is mid-12c., also Biblical. Meaning "strike with passion or emotion" is from c.1300.