c. 1600, "to select by lot and put to death every tenth man," from Latin decimatus, past participle of decimare "the removal or destruction of one-tenth," from decem "ten" (from PIE root *dekm- "ten").
The killing of one in ten, chosen by lots, from a rebellious city or a mutinous army was a punishment sometimes used by the Romans. The word has been used (loosely and unetymologically, to the irritation of pedants) since 1660s for "destroy a large but indefinite number of." Related: Decimated; decimating.