1580s (transitive and intransitive), not found in Middle English, probably from a Low German source such as Middle Dutch splitten, from Proto-Germanic *spleitanan (source also of Danish and Frisian splitte, Old Frisian splita, German spleißen "to split"), from PIE *(s)plei- "to split, splice" (see flint).
U.S. slang meaning "leave, depart" first recorded 1954. Of couples, "to separate, to divorce" from 1942. To split the difference is suggested from 1715; to split (one's) ticket in the U.S. political sense is attested from 1842. To split hairs "make too-nice distinctions" is from 1670s (split a hair). Splitting image "exact likeness" is from 1880. To split the atom is from 1909.