Normally, we do not want to see the quick navigation on the left side of the homepage, but on other pages is useful, as above menu remains always the same, this can be easily done using JavaScript or JQuery code.
Click on the edit page and insert a new Web Part called Script Editor from the group Media and content.
source: enjoysharepoint.com
It does not remove the entire field, but only hides the quick navigation menu.
I have not tested, but I think that the code works as well in lower versions of SharePoint Server, not only in SharePoint 2013.