If you’re spitting it from your mouth or blowing it through a straw you don’t need to remove it from your mouth. Just launch. If your weapon is to throw it, take it out of your mouth first. Once you’ve soaked your spitball with spit, you can take it out of your mouth and launch.
Put the spitball between your thumb and middle finger, pull your arm back, aim, and throw.
You might need to be standing close to your target for this launching method to work.
Put your spitball inside of a straw, pushing it in as far as you can. Take a deep breath and put your mouth on the straw so no air can get in. Blow as hard as you can. Your spitball should pop out of the other side of the straw, right at your target.
Curl your middle finger into your thumb to form a circle, so that the nail of your finger is touching your thumb. Press them together so there is tension between your fingers. Put the spitball in the spot where your middle finger meets your thumb. Right between them, on the outside of your middle finger. Push your middle finger out, away from your thumb. This should make the spitball fling up and out, toward your target.