If you are a group moderator / creator, you can expel a member, which would block them from that group. If someone violates the terms of service, they can be reported and deal with by the site administrators. If they are just saying disagreeable things, however, that is not enough. The terms of service is at the far right hand lowest corner of the page.
If you are following a post in the forum or on a group, you can unfollow. Then you don't get any updates on that topic. I do that sometimes when it becomes tedious. You can also close your own topic. That is responsible, if you are not up to monitoring posts, or are tired of the topic. If someone else wants to continue the topic, they can start their own post and link to yours.
More than that I'm just guessing about whatever the situation is.