You can use the git update-ref command. To remove the last commit, you would use:
$ git update-ref HEAD HEAD^
Or if you’re not in the branch from which you cant to remove the last commit:
$ git update-ref refs/heads/branch-name branch-name^
You could also pass a sha1 if you want:
$ git update-ref refs/heads/branch-name a12d48e2
See the documentation of the git-update-ref command.