You cannot branch out between servers (or project collections) in TFS.
Need to upgrade to a new server? In this case, restoring a backup of your current server to a new server and deleting Team projects that you do not need may be a solution. If you need to "merge" the code back to the source server, at some point you can watch TFS Integration Tools . This will allow you to move the code to a new server, as well as synchronize the code.
However, there are limitations with the toolkit, see the link for more information.
Why do you need a new server? Why is it not necessary to have a new branch in the current Team Project?