If you wish to view the essay responses you've submitted during a full length practice test, you can do that on the Review screen.
One you're on the Full Length Test review screen, choose the tests that you wish to review. and click the corresponding 'Review' button at the right end.
After you click on the 'Review' button and view the review screen, you can view your AWA score on the top left, and just below that is a link that says 'View AWA Responses'. Click that and you'll be able to see and copy paste what you wrote.