Unfortunately this is a known issue, and not possible to overcome in todays version:
There are some group policies that control the Backstage area, but they are mostly all or nothing, removing all SharePoint referencing not just the Office 365 ones.
The workaround below should remove the O365 SharePoint on line content from the Office Save As screen ...
I would probably do it with a new document library where the files can be moved to. Permissions would be add only (a custom one to create) and set the library properties to exclude it from search. Then you could create a workflow upon marking the document as "complete" it moves it to the library and then deletes the current file.