When dealing with SPAM comments on your blog, one of the foremost considerations should be whether those links in the comment (that people are leaving) are noFollow or doFollow.
You don’t want to pass on your link juice and PR to other websites. So, make very sure that all the links in the comment section are ‘nofollow’. This value commands the search bots to NOT crawl the encountered links. So, the commenters who leave the links of their websites for SEO-purpose, they are NOT benefitted now.
With this being done, I don’t think you should care a lot about the kind of comments your posts are getting. Unless, of course, they are very offensive. The number of comments usually reflect a high-engagement rate, which further tempts others to join the conversation. For instance, on Facebook, when you see a post with more comments, don’t you want to engage with that post even more and leave your comment there? (Exactly my point!)
However, if you really want to deal with spam comments on your blog intensively, there are many easy ways. A simple solution is to use a robust commenting system. Disqus is one of the leading names out there. LiveFyre and IntenseDebate are decent platforms as well. Also, even Facebook provides a commenting system (I don’t recommend it though; slows down the website).
Having used Disqus myself, the platform is very robust with plenty of options and higher flexibility. You can set it in the option that a person without a verified account cannot comment on your blog. You can block anonymous comments. You can make all the links in the comments ‘noFollow’. You can ban words. There are plenty of features—all coming at free of cost. Also, Disqus provides a handful of interactive features that can actually enhance engagement on your website.
So, to effectively deal with spam comments on your blog, I would say use one of such robust commenting systems; Disqus preferably.
In case, if you’re using a CMS like WordPress, Blogger or Joomla, get rid of their default commenting system.
Hope the answer helps!