When you are on the connection finder view, and you see the whole line of people connecting you to the Mayflower passenger, you can click the small "x" (top right) on any person, and the connection will be re-configured without that person. If you want to see a blood-relation connection, instead use the Relationship Finder. (You can go to, say, Richard Warren (1583-1628), then hover over Warren-66 at the top right, and click Relationship to Me.