You can do this, if the remote repository accepts forced pushes:
git push --force origin clean_start:master
Note that if anyone else has the repository cloned, a push from them could potentially undo this. If you want to merge your local master branch and the remote master branch, but keep the file tree from your branch (discarding the file tree of origin’s master), you can do so like this:
git merge -s ours --no-commit origin/master
git commit # Separate step so that you can use your own commit message.
git checkout master
git merge clean_start # Fast-forward
git push origin master
This will create a merge commit with both branches (your master and origin’s master) as its parent, but the tree will be identical to your current branch tip. In other words, it will create a symbolic merge where no actual code merge occurred.
If you don’t mind that other people working in the repo will be interrupted, you can use the first approach. But if you work with other people who already have these commits, the second approach will be more fool-proof and will keep history.