Problem

You would like to remove your local branches that were used to track remote branches that no longer exists (deleted after merge).

git branch -a
branch_to_delete
remotes/origin/branch_to_delete

Solution

To delete your local branch you could use the following:

git branch -D branch_to_delete

And to to delete the remote tracking branching you could use the following:

git branch -rd origin/branch_to_delete