If you shoot at something that is falling... it's still gonna fall, even if you hit it, brrak it up, etc. Whatever matter is there before will still be there after the hit, but on a less predictable trajectory.

If you break it up into pieces before it re-enters the atmosphere, you may get a higher proportion of burnup, because small chunks means lower overall ballestic coefficient per mass... But hitting stuff in orbit is difficult, and we would have a very hard time predicting the results.

There's a diplomatically-sensitive moratorium on shooting down space objects. Technically, sure.

https://www.reuters.com/world/us/us-will-not-conduct-direct-...