In the desktop version, if you hover over their name in the in-dash notification you'll get a pop-up. Click on the little person icon and "block".

Slightly longer way: copy their name, go to Settings, click on your blog name, scroll down to "Blocked Tumblrs", click on the pencil/edit icon, and paste in their name. (Or you could retype it there. I usually c&p to make sure I get it exactly.)