It's obvious. Resetting the search index clears all search results. It does however not remove all crawled and managed properties. SharePoint (2013) remembers them forever.
The only option to remove them entirely is to provision a new search service application. This can hardly be the best tool for the task.
How do YOU get rid of old/invalid/orphaned search index properties?
I know you can remove a managed property to crawled property mapping. And then go forth and "delete all unmapped crawled properties" or whatever it is called. In my opinion this never did anything useful.