Duplicating a dashboard doesn't duplicate the worksheets it contains. Any changes you make to the underlying worksheets will be reflected on the original dashboard and its duplicate.
Thanks for the update.
If there is any possibility, making changes to the Filter affects the worksheet as weel
What is your objective in duplicating the dashboard? If you intend to keep both and filter them differently somehow, you might want to duplicate the worksheets and have two dashboards that look the same but function independently.