Yes. Click the tag and it will pop up with a list of posts using that tag recently. On the top left, there are two options. Click "follow tag" if you want to see all posts with that tag. Click "filter tag" if you want to hide all posts with that tag.
I might caution you though to be selective with your filtering. You might miss out on some great posts that you'd otherwise might be interested in if you filter too many categories. People here love to multi-tag.
The same can also be done for users. For example, I filter out all spam posters. To do so, you click on a user's profile and to the left will be the option to follow them. On the very bottom left of their profile, you'll see three different filter settings which are pretty self explanatory. Once again, I caution against liberal use of these settings, as you might miss out on some good discussions. Just because you don't always agree with someone, doesn't mean you should remove them completely from your feed.
As an aside, since we're talking tags, you'll also notice sometimes a post will have a third tag, that's a tag suggested by a community member.