By default deleting a site collection in Office 365 just moves the site collection to the recycle bin for 30 days, but there is not an option in the admin screen to remove it from the recycle bin.
This is fine, unless you want to use the same url for a new site collection. In this instance you will need to use PowerShell to remove the site collection from the recycle bin. To do this you will need to install the following.
PowerShell v3.0
http://www.microsoft.com/en-us/download/details.aspx?id=34595
Microsoft Online Services Sign-In Assistant for IT Professionals RTW
http://www.microsoft.com/en-us/download/details.aspx?id=35588 or http://www.microsoft.com/en-us/download/details.aspx?id=39267
SharePoint Online Management Shell
http://www.microsoft.com/en-us/download/details.aspx?id=35588
Once this is done open up the online management shell and enter the following.
Connect-SPOService “[Full Admin URL]” -credential “Online User Id”
Remove-SPODeletedSite “[Full URL]”
