A while back we had a Twitter conversation with @AutodeskHelp and @TommieR on UNinstall procedures for various Autodesk products. Autodesk has published articles regarding the removal of Civil 3D 2009, 2011, and 2012. For whatever reason, there is nothing on 2013, and the articles that do exist do not cover the removal of every component installed with Civil 3D
Recently we had the task of performing a few Uninstalls of Civil 3D 2013 and the order of Uninstalls shown below seems to work successfully. This is not the only order that will work, but there are certain things that must occur. For example, you have to remove the Storm and Sanitary Analysis Plug-in before removing the Storm and Sanitary Analysis component itself.
2014 versions and later include an Uninstall Tool, which is noted in the Twitter conversation linked to above.