The “Sign in as Different User” option that was present in SharePoint 2010 has now been removed for SharePoint 2013 (I assume because it caused a lot of confusion between Internet Explorer and Office if you were logged onto the PC under one account and into SharePoint as another).
You can get around this by visiting http://siteurl/_layouts/closeConnection.aspx?loginasanotheruser=true
Source: “Sign in as Different User” menu option is missing in SharePoint Server 2013