Having had outdoor cats for a few decades, I gotta agree with ValGal to some extent.
Our cats usually enjoy the fruits of their labor in private and the leftovers are found in the back corner of the garage or under a bush, depending on where they decided to have their picnic.
The "front-door gifts" have been fully intact, albeit demised, creatures in the form of birds, chipmunks, mice, etc.
I don't recall every having been gifted just pieces and parts.
I'll agree that it *sounds* like a cat, but the pieces and parts is not prototypical in my experience.