If you choose NOT to mirror then you will notice that your second monitor is an empty desktop without icons and without a panel. Cinnamon version 2.6 and later support applets and panels on the second display. You can add a panel to your second monitor by doing the following: Right-click the panel on your primary monitor and select "Modify panel" and "Add panel." The top and bottom edges of all monitors should get highlighted and a new panel will be set up where you click.
The menu and applications will align right on the second panel on the second display. You are supposed to be able to change this by choosing to enable panel edit mode and drag and drop the Window list to the left side of the panel (red colored). However, like many things in Linux this is broken. Maybe it will be fixed on the version of Cinnamon that you are using.
Issues like the annoying application thumbnails and the alignment of the Window List applet can be customized: