Middle English quellen "to kill" (a person or animal), from Old English cwellan "to kill, cause to die; murder, execute," from Proto-Germanic *kwaljanan (source also of Old English cwelan "to die," cwalu "violent death;" Old Saxon quellian "to torture, kill;" Old Norse kvelja "to torment;" Middle Dutch quelen "to vex, tease, torment;" Old High German quellan "to suffer pain," German quälen "to torment, torture"), from PIE root *gwele- "to throw, reach," with extended sense "to pierce."
The original sense is obsolete; the milder sense of "suppress, extinguish, cause to cease," developed by c. 1300; that of "reduce to peace or subjection" is by 1560s. Compare quail (v.). "The common identification of quell with kill (1), of which it is said to be the earlier form, is erroneous" [Century Dictionary]. Related: Quelled; quelling.