I am supposed to have a cervical polyp removed first thing in the morning, but am at the tail end of my period (only used the thinnest smallest pad all day today, but I did need a pad). Should I reschedule the procedure?

No, it wouldn't usually be necessary. Many women will have polyps removed because of that very reason; they are bleeding too much or continuously, so the bleeding won't be an issue.

You can always give your doctor a call first thing to inquire as to their preference.