You can also delete the branch on the remote directly. Having done that, the next update will remove it from your working copy.
svn rm "^/reponame/branches/name_of_branch" -m "cleaning up old branch name_of_branch"
The ^
is short for the URL of the remote, as seen in 'svn info'. The double quotes are necessary on Windows command line, because ^
is a special character.
This command will also work if you have never checked out the branch.