"tear apart," c.1400, probably of North Sea Germanic origin (cf. Flemish rippen "strip off roughly," Frisian rippe "to tear, rip") or else from a Scandinavian source (cf. Swedish reppa, Danish rippe "to tear, rip"). In either case, from Proto-Germanic *rupjan-, from PIE root *reup-, *reub- "to snatch." Meaning "to slash open" is from 1570s. Related: Ripped; ripping.
Meaning "to move with slashing force" (1798) is the sense in let her rip, American English colloquial phrase attested from 1853. The noun is attested from 1711. The parachutist's rip cord (1911) originally was a device in ballooning to open a panel and release air.