See man git-fetch, section “PRUNING”.

At one time, I had a couple dead remote tracking branches:

$ git branch -r
  origin/HEAD -> origin/master
  origin/WIP-syscall
  origin/master
  origin/proc-cmdline

On the next fetch, if the upstream branches no longer existed, delete the tracking branches:

$ git fetch --prune
From https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux
 - [deleted]                   (none)     -> origin/WIP-syscall
 - [deleted]                   (none)     -> origin/proc-cmdline
$ git branch -r
  origin/HEAD -> origin/master
  origin/master
$

$ git remote prune <name>