Q. Want a menu that only displays submenu items?

A. Change your CSS file so it will not display mainlevel items.

.mainlevel { display: none; }

When
you are using a separate main and submenu make a copy of the main menu
module. The copy should be named submenu and you should give it a class
suffix. (for example _sub).

When doing so the css should be as follows:

.mainlevel_sub { display: none; }
.sublevel  { display: none; }

The main menu will only display main items now.
The submenu only displays submenu items.

With the position setting, you can adjust the location where both menus will be displayed.