You just delete the branch in your local repository.The branch in drop down is on the remote(TFS server)
From Visual Studio you have two options:
1.Unpublish
2.Delete
Unpublish will remove the Branch tag on the remote (TFS server) and that will hide the branch from the drop down.The branch in local still exists.
Delete will remove the branch from your local TFS repository. It will remain on the remote (TFS Server), but you will no longer have it available in your Visual Studio's Branches window. You can get it back by creating a local branch that tracks the remote branch anew
So ,to achieve what you want, you just need to unpubilsh the branch or delete the branch from remote.
More info from Microsoft: https://msdn.microsoft.com/en-us/library/jj190809(v=vs.120).aspx (reference remove branch)