This is the expected behaviour.  The Process could be approved or declined by others, and it remains on the Dashboard until you either approve, or the Process is edited and saved again.  

If you would like the notification to be removed and removed from all other approvers dashboard, you can edit the Process and save it, then the approval process will stop and start again from scratch once it is submitted for approval again. 

But if the only two approvers are the author of the map (Owner) and me (Expert), should it not fall off since there are no outstanding approvals?  Or does it remain because of the discrepancy between the Owner's approval and the Expert's decline? 

I agree and have, I think, raised there somewhere else on this website. When I decline a process as a publisher, and Im the only approve the expected result should be it dissapears back to the developer. Although this is expected in terms of how the system has been designed, its not expected in terms of a user experience. Cheers

At this stage, the way the application works, is any "Decline" does not remove the Process from the approval workflow, so it remains on the dashboard. 

As Anthony has said there have been some User Voice suggestions for changes to this feature, and you can comment/upvote these ideas here - our User Voice page is monitored by our Product team who make the decisions building out the application. 

https://nintex.uservoice.com/forums/919189-7-nintex-promapp/suggestions/38338072-declining-approval-or-publishing-request-by-at-lea
https://nintex.uservoice.com/forums/919189-7-nintex-promapp/suggestions/38379361-remove-declined-processes-from-the-publish-list