I agree with the others that this was probably some type of raptor. An animal that is able to carry the duck away, e.g., a dog, will typically take it away. You also wouldn't normally see the type of thing you describe with a mammal, whereas raptors will be able to pick the bones completely clean because they have sharp beaks. If you have a pic or can get one, you can PM it to me.
May I ask how long it had been since you had seen the duck? Was it just the night before? It is possible to have multiple predator attacks that cloud the diagnosis. For instance, you could have an owl that killed the duck, but owls will typically take only the head. Once the animal is dead, raptors that feed on carrion, e.g., vultures, come and finish the job. They can pick a bird like a Rouen clean in a matter of minutes.
What I'm about to say isn't meant to be unkind. It's only to impress upon you how horrible this is. Please take a couple of minutes to imagine in your mind what the duck was subjected to when it was killed. Since you cared enough to post about this, I know you're not going to want any of your other ducks to be subject to such a horrible, agonizing death. If you want to keep them safe, you have to find some way to get them into some sort of shelter during nighttime hours. Even your screened porch is preferable to nothing while you're working on a long-term solution. Poop is an issue with any living thing, but poop can be cleaned up.
