From the WordPress.org Support forums:

I need to prevent my default category from appearing in the list of category links. Is there a way to hide the default category title, but still display all posts when the user clicks the “blog” (show all) tab?
biodrama

You can use a little CSS added to the end of your style.css file to stop a category title from appearing in the list, in your example, the “Uncategorized” default category can be made to not show up with:

.cat-item-1 {display:none;}

If you want to use a different default category, finds its ID and replace the ‘1’ above accordingly.