First of all, there is no way to do this using the GUI, You have to rely on the PowerShell. there are 2 options in Powershell.
use the [Copy-Spsite][1]Copy-Spsite
Copy-SPSite http://contoso/sites/OldTeam -DestinationDatabase WSS_Content -TargetUrl http://contoso/sites/NewTeam
- Now Run the Remove-Spsite to remove the old site.
Another option is Using the BackUp and Restore
- use Backup-spsite to get the backup
- Now run the restore-spsite to restore on New URL
- Now Run Remove-Spsite to remove the old site.
At the end you have to run the Search crawl so that old content removed and new added. [1]: https://technet.microsoft.com/en-us/library/fp161280.aspx