I've found some suggestions in this forum on how to do this:
"open single.php and remove from line 73:
Delete: <?php comments_template(); ?>
You could also remove line 45 which shows the comment count since this is no longer needed. Same goes for line 60 in template_blog.php :)"
So, I've deleted the two lines in single.php and the one line in template_blog.php file in the Clean Cut theme. If you look at my test site: http://renaissancebloke.com/singularsoftware/blog/ the "No Comments" box to the right of the date has gone.
However, if you were to click on any of the blog category links e.g. "Third Party Blogs" http://renaissancebloke.com/singularsoftware/category/third-party-blogs/ then the "No Comments" blog shows up again so there must be another line somewhere that I need to remove, I'm just not sure where it may be.