Send as many troops to the border area as it takes to convince the Mexicans that we are ready to invade. Start blowing up the infrastructure in Mexico that leads to the border. The Mexicans will stop the caravans at that point. No body dies on purpose.
Works for me. This is at least a warm WAR. Polite responses are likely suicidal past a certain point. We do not need to become evil in our response but we don't have to be idiotic wimps, either.