This is a limitation of the tool - but there is a workaround.
If you are just looking to copy the dashboard in the same organization (I didn't test between organizations, but it should work as long as you duplicate the map and then update the JSON to point to that map).
So - what I did is to just create a new dashboard (can be blank) and then in the AGO Assistant tool, go to 'View an Item's JSON' - now, copy the JSON in the Data section - and then paste it into your 'new' dashboard. This will copy all of the configurations, etc. over.