In my current repo I have the following output:
$ git branch -a * master remotes/origin/master remotes/public/master
I want to delete <
All you need to do is
git fetch -p
It'll remove all your local branches which are remotely deleted.
If you are on git 1.8.5+ you can set this automatically
git config fetch.prune true
or
git config --global fetch.prune true