Here's a handy GIT alias to trim off old branches, keeping your repos clean and tidy.
Add this alias to your git config. It's a bit complex, so you will need to do it by hand.
[alias] trim=!sh -c '[ $# = 2 ] && git branch -d "$2" && git push "$1" :"$2" || echo "Usage: git trim <remote> <branch>" >&2 && exit 1' -
To use it, just specify the remote and the branch name:
$ git trim origin my-old-branch
This will delete
my-old-branch locally and attempt to delete it from the remote as well.