If one person shoots down another, they shoot them with a gun. He was prepared to suppress rebellion by shooting down protesters They shot him down in cold blood
If you shoot someone down or shoot down their ideas, you say or show that they are completely wrong. She was able to shoot the rumour down in flames with ample documentary evidence
If someone shoots down an aeroplane, a helicopter, or a missile, they make it fall to the ground by hitting it with a bullet or missile. They claimed to have shot down one incoming missile