Yes, JetBlue can cancel individual tickets on a reservation but I believe you need to call in to do it so they can first split off the passenger or passengers that are cancelling. No way to split online.

JetBlue, like all airlines, will sweep passenger manifests occasionally and cancel duplicate or overlapping bookings. But as long as you call to cancel the original ticket or tickets immediately afterwards (reminding them to leave the remaining tickets on the original reservation in place), you shouldn't have an issue. Just don't plan to wait a day to cancel the original or they could cancel the new one with the MTM certs. I've had duplicate bookings a few times on JetBlue for brief periods (e.g., switching from cash to points booking or vv) and it's been fine.