In the Vertical Menu it is quite easy to set if you would like to only show a part of the whole menu structure you have selected. That could be useful if you have a big menu structure, and wouldn't like to show all of the levels, as that can confuse the users.
You should open the Module Manager of your Vertical Menu, open the Advanced Parameters tab, and enable the Improve level handling parameter. Then you will see that 2 parameters will be visible, Start level and End level. The first level can be set by '0', so in case of you only would like to show the menu from the 2nd level, then you need to write '1' into the Start field. The end level works in the same way, you need to write the correct number of the ending level.