"to make void, annul," early 14c., from Old French quasser, casser "to annul, declare void," and directly from Medieval Latin quassare, alteration of Late Latin cassare, from cassus "null, void, empty" (from extended form of PIE root *kes- "to cut").
Meaning "to break, crush," is early 14c., from Old French quasser, casser "to break, smash, injure, harm, weaken," from Latin quassare "to shatter," frequentative of quatere (past participle quassus) "to shake," from PIE root *kwet- "to shake" (source also of Greek passein "to sprinkle," Lithuanian kutėti "to shake up," Old Saxon skuddian "to move violently," German schütteln "to shake," Old English scudan "to hasten").
The words have influenced each other in form and sense since Medieval Latin and now are somewhat grown together. Related: Quashed; quashing.