I like to housekeep my blog and my computer, to help them run more smoothly and quickly. When Google Reader was still operating, removing a blog was easy and straight forward. Today, I decided to remove some blog's that are no longer active, only to face more than an hours search to find how to do it. It used to be so easy!
Firstly, go to your dashboard, in the section that says Reading List, right click on the gear wheel on the far right of that particular section (not the one at the very top of the page). By right clicking you should then choose "Open in a new tab" which will help you work two screens at once.
It will bring up a new screen "Manage Blog's I'm Following". Go down to the blog you wish to remove, click on the dustbin symbol on the right (it might take a few seconds for the blog to disappear):
All you need do now, is to go to layout, make sure you remove them from there, if they are still showing, and you are done.
I hope this has been of use to you.