Does destroying ballots invalidate an AGM vote?

I couldn’t possibly be definitive based on your short description of the situation.

What I would say, though, is that voting at a body corporate meeting can be a challenging process, with many moving parts. If one part does not go according to legislation, or appears not to, then that does not automatically mean the result is invalid. It might, for example, depend on how the numbers went at the meeting. If the vote was 90 ‘yes’ and 2 ‘no’, then it’s extremely unlikely the allegedly ‘destroyed’ votes would make a difference. Then again, if the vote was 47 ‘yes’ and 45 ‘no’, then that’s a very different story. I recommend you consider this aspect of the situation before taking any further action.

Note that you have 3 months after the meeting in which to challenge the result. You would need to demonstrate, based on objective evidence, which part of legislation was not complied with, in your view.