In SharePoint 2013 environment when you try to save a publishing site as sitetemplate you should get the following error message “The “Save site as template” action is not supported on this site".
In order to enable this, we can use either SharePoint Designer or PowerShell. In this blog, I will be taking the help of PowerShell to solve the problem.
Add-PSSnapin Microsoft.SharePoint.PowerShell
$site = Get-SPSite -Identity
http://mysites/publishingsites
$web = $site.RootWeb;
$web.SaveSiteAsTemplateEnabled = $true;
$web.Update();
Now you can redirect to see your publishing site saved as a template.

/_layouts/savetmpl.aspx

Or

/_layouts/15/savetmpl.aspx

Happy Share Pointing :-)