When you run a campaign on a database for the first time, SAM adds 2 Contact fields to that Act! database. One holds the stage of the contact for the campaign, and the other holds the date that the campaign was last run on that contact.
To remove a campaign from a database, you do the opposite...you go into your Act! database and delete those 2 fields.
When you remove the fields it's also good to remove them from your Contact Layout (if they were added). Then you can also delete or archive the campaign (CMP) file in your SAM campaigns folder if you aren't going to reuse it. By default this location is in your Documents\Northwoods Software\Sales Automation Manager\Campaigns folder.
The next time you run a campaign in SAM you will no longer see that campaign listed.