You will need the Full Write Connections permission to perform this action.
There are two ways a connection can be deleted.
From the Connection
Navigate to the connection record either from the main connection listing or from the person's profile from within the Involvement > Connections tab.
Then select "Delete" from the "Actions" menu in the top right.
From the Person's Profile
You can also delete a connection right from the associated person's profile. Navigate to the profile, and click on the "Involvement" tab. Then select the "Connections" tab. Finally, select "Delete" from the drop-down menu at the end of the row containing the connection you want to delete.
Regardless of which method you use, a confirmation message will appear. Click on "Yes" to finish deleting the connection.