There are two ways you can remove the duplicates from the Campaign.
Option 1 - Manual
Once the campaign members have been added to the respective campaign. Select the 'Remove Duplicate Campaign Members' button from the action list on the Campaign details page which will remove any duplicates. You will receive a confirmation email with the results.
Option 2 - Automatic
You can set up the auto suppress duplicate emails option by navigating to MassMailer Setup -> Email Settings -> and turn on the 'Suppress Duplicate Emails' option.