The action of something being forced or thrown out is called ejection. If you notice an ejection of black smoke from your car's tail pipe, you'll probably want to take it to a repair shop.
There is the physical kind of ejection, when a substance or object is propelled or projected away from or out of something else, like the ejection of a bullet from a gun or the ejection of lava from a volcano. Another kind of ejection happens when someone is instructed or forced to leave, like the ejection of a rowdy customer from a bar or an unpopular politician from public office. The Latin root, eicere, means "throw out."