Welcome.
I've enabled the negative reputation feature in order to allow my users to moderate forums themselves. The problem is that I can't find an option to force hiding posts with a certain negative reputation level.

I know there's a filter for users, but can it be done automatically through an option?

No, it is a per-user option.

AnthonyKinson has a mod that does something like this.
Search is your friend, as he was just talking about it here a week or so ago.