Was there any visible trauma to the swan, i.e., neck or foot, leg, body injury? It is not likely a snapping turtle is going to kill a swan intentionally, but could snap at a leg or other body part and leave a gash. If there is no visible injury, she may have died from old age, sickness or poisoning.

Males do sometimes care for the cygnets, but it is usually the female that is responsible for the task. If the male shows no caretaking duties (he leaves the cygnets alone to fend for themselves as he goes to the other side of the pond or far away from him), then the cygnets are not going to survive. They should be about 3 months of age and this is still not old enough to fend for themselves. If the cygnets do survive to 6-7 months of age, then the male swan will chase them from the area.

If he is able to chase them (we are presuming that the birds can fly - not pinioned), then you either have a wild swan or a swan that is responsible for a feral population. If this is the case as in the Mute Swan, the cygnets may be killed by your state and fish commission as any non-native species found in a feral population can be killed in many states. If you are planning to intervene and take the cygnets, you need to ascertain the species and if you need a permit. If they are wild indigenous swans, Trumpeters or Tundras, you probably cannot intervene. If they are Mute Swans (non-native), you will possibly need a permit for possession and the cygnets will need to be pinioned to keep them from flying from your pond. The Regal Swan