Hello N,
"Copy and rename it." Why would you want to do both?
You can rename the blog, and delete the posts, if you do not care about them any more.
Or, you can download the blog theme, create a new blog, and import the saved theme. Then start blogging.
This is of course creating "a new blog from scratch," but it is straightforward and preserves your original blog.
If you do both, you will have two identical blank blogs.