Note: Contacts were added in the Default Mailing List. With the help of the triggers we were also able to clone the contacts when we cloned the campaign record.
Step 1: Create a New Field on the Campaign (Hidden from the users).
Data Type: Text
Navigation: Customize > Campaigns > Fields > New
Step 2: Create a Validation Rule
Navigation: Customize > Campaigns > Validation Rule
Step 3: Create a Workflow Rule
Navigation: Create > Workflow & Approvals > Workflow Rules
Workflow Actions > New Field Update
Activate the workflow rule.
Step 4: Clone the existing campaign record using same campaign name. Hence we are getting the error. We need to change the Campaign Name to save the record.