Log in and click on your assignment. Go to the "grading" tab. Each graded essay will have a "public link" next to it. But instead of clicking on a graded essay's "public link", right click (or CTRL-click on a Mac) on the link and you should see a "Save link as" option or something similar (it varies by browser).
Each graded essay is an HTML file that can be saved to your computer. Once it's saved to your computer you can just double click on the saved HTML file. It'll open in a web browser, except it'll be accessing your local copy. This would allow you to keep a digital copy of the graded work on your computer that would be accessible even without an Internet connection.