The word "stalker" is a legal term that applies only if your are referring to someone in real life. It does not apply to those who have public blogs, which are open to everyone on the internet to read, to subscribe to and is open to comments.
We cannot block or delete subscribers from public blogs. However, please read this about public blogs that become private blogs > Blog Privacy and Subscribers > http://wpcommaven.wordpress.com/2011/09/05/blog-privacy-and-subscribers/
Note that we have complete control comment moderation. http://en.support.wordpress.com/settings/discussion-settings/#comment-moderation If your blog is public others can, of course, read it. They can submit comments but you can Moderate all comments and choose which ones to approve or not.
For trolls, you can “blacklist” them at Settings > Discussion toward the bottom of that page. Enter their email address, their username, and if they included it, their website. That will automatically send them to moderation so that their comments do not appear on the blog. Do note though that if they are determined, they can use a different email address or username to get around that.
Also, do not put their IP address in the blacklist. IP addresses are no longer unique, and you might end up blocking legitimate visitors as for many years now ISPs have been saving money by placing hundreds of us in the same IP block. Also, all they would have to do is go to a wi-fi hot spot, or connect via a different ISP and they could get around that.
One other thing I would suggest is to set your blog so that first time commenters are held in moderation till approved, then from that point forward they will not need approval. Settings > Discussion. The next step on that of course is to set it so that all comments are held in moderation until approved. That way you are in control, and they might just get tired and go elsewhere after a while.