Thanks for the report. I can confirm that this is a bug, but only when not using official final releases. It appears that the problem is that we are ignoring the .dev0 portion of the version used for the previous deployment. At mkdocs/commands/gh_deploy.py#L61-L62 we have:
Note that the regex for the "previous version" does not capture .dev0, but only 1.1 from the full version 1.1.dev0. Therefore, pkg_resources is reporting (correctly from its perspective) that 1.1 is greater than the "current version" (1.1.dev0). Of course, we should be capturing and passing in 1.1.dev0 for the "previous version," which would correctly result in the previous and current versions being equal.
To fix the issue, we need a more complete regex to capture the entire version string. All allowed version strings and the proper sort order is defined in PEP440. Presumably, the regex would capture anything allowed there. Its important to note that "pre" ("alpha," "beta," and "release candidate") and "post" releases, which could all be official releases would also exhibit this bug, so its not just the dev version and warrants a proper fix. That said, MkDocs does not make a practice of doing "pre" and "post" releases, so the priority is not as high as it might be otherwise. Of course, a PR is welcome as always.