Will my bb gun shoot out a tire?

Nope. And as Tahoe said, they will bounce back. I saw a guy shoot a tire on an abandoned car with a .38 Special loaded with light target wadcutters (he said he reloaded them himself). The bullet bounced back and smacked him in the shin. He was hopping around with both hands wrapped around his leg (he had dropped his revolver) screaming "I've been shot! I've been shot!" I got him settled down and sat him on a stump and pried his hands off his leg. I said "Well, you can't be too shot. There isn't a hole in your jeans." He was bleeding though. Definitely left a mark.

This story dosn't have much to do with the answer but the question gave me a flash back and I had to share it.

does it shoot metal or plastic bb's, personally i dont have a bb gun but it would depend where you hit the tyre as the tread is alot thicker than the sidewall and also if the tyre is highly pumped it has a better chance of putting a hole in it than a flat tyre.

If it is a bb gun, and not an air-soft gun, then yes it will.

Not a chance in the world. Absolutely none.

I mean 'zero' chance. But its not really safe to do, they bounce back.