Should I mention my blog in my SOP?

Yes. You could mention it in your SOP and/or in your CV.

I have received some applications from students in which they mentioned a technical blog, and so far it has always left a positive impression. In my opinion, keeping such a blog demonstrates:

  1. Maturity in writing and communicating (especially if your blog communicates something technical in an informal way that is not sloppy).
  2. Organization of thought and effort.
  3. Initiative.
  4. Love for learning ideas relevant to your discipline.

In a notorious question in Academia.SE, JeffE has stated this:

  • What have you already done? What problems have you solved, or at least worked on? What independent projects have you been part of? What were your key contributions? What did you learn? What did you teach the world? How do your results compare to what was already known? What original ideas are you most proud of? Be specific, technical, credible, and confident (but not arrogant). Refer the reader to your web page for more details. Have a web page with more details: preprints, project reports, source code, videos, etc.

So yes, yes you can.

However, personally, I would like to mention it in my CV.