"pull apart," Old English teran "to tear, lacerate" (class IV strong verb; past tense tær, past participle toren), from Proto-Germanic *teran (source also of Old Saxon terian, Middle Dutch teren "to consume," Old High German zeran "to destroy," German zehren, Gothic ga-tairan "to tear, destroy"), from PIE root *der- "to split, flay, peel."
The Old English past tense survived long enough to get into Bible translations as tare before giving place 17c. to tore, which is from the old past participle toren. Sense of "to pull by force" (away from some situation or attachment) is attested from late 13c. To be torn between two things (desires, loyalties, etc.) is from 1871.