A mink could have killed the young cygnets as well as owls, hawks, snapping or soft-shelled turtles (if you have them), fox or any other type of predator.

If the cygnet was on the mother's back, the cygnet could have been sick and all cygnets may have succumbed to an illness, with this last cygnet finally dying.

It is difficult to say what the problem might have been, a combination of both or none without having looked at the remaining cygnet. We're not sure where exactly you are located, but if you are near or can ring the Swan Lifeline, in Eton, England, we would suggest that you speak with Wendy Hermon to see what she might think. Wendy rescues a lot of swans, especially along the Thames and she may know the area that you are located and offer some insight. The Regal Swan