In military and other covert operations,
terminate with extreme prejudice is a
euphemism for aggressive execution (playing on the expression "termination with prejudice" of an employment contract). In a military intelligence context, it is generally understood as an order to
assassinate. Its meaning was explained in a
New York Times report on the
Green Beret Affair (an incident during the
Vietnam War), and subsequently popularized by use in movie
Apocalypse Now.