There are actually three ways the alcohol leaves the blood stream. The first way is that the lungs exhale 5 percent of the alcohol, the second way is that the kidney eliminates some of the alcohol thru urine, and the last way is that the liver chemically breaks down alcohol into acetic acid. To answer your question, the organ that has the primary responsibilty to eliminate alcohol from the blood stream is the liver because it chemically breaks down the alcohol into acetic acid.