"to hit, strike, give a hard blow; beat with the hand, a stick, etc.," late 12c., smiten, 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, smiton). This is from Proto-Germanic *smitan (source also of 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.
The word was formerly derived, as 'he that smiteth' (sc. with the hammer), from smite, v.; but this is etymologically untenable. [Century Dictionary]
It is attested by c. 1200 as "strike with any sort of weapon." The sense has been extended by Biblical use, which accounts for the now somewhat archaic meanings "visit disastrously, bring about affliction, etc." (c. 1200), "slay in combat, destroy the life of" (c. 1300, from Biblical expression smite to death). The figurative meaning "touch the heart, strike with passion or emotion" is from c. 1200.