You can't directly "copy" a tree, but you can duplicate it. To do so, click on the "Download" button on the bottom of your screen and download your current family tree. If you go to your "My Account" page (upper right side of the screen) you can select "Create or import a new family".
After you have created a new family, you'll see the option "Import GEDCOM or FamilyScript" on the bottom left side of your screen (beneath the buttons for "Add parents", "Add partner", "More Options" etc.). Now you import the file you have saved and have effectively copied your original family.
Hope this helps!
