To kill the spirit turtle, you have to both destroy its head and its heart, as they are basically familiar cores for the Spirit Turtle. Without its head, it is basically stunned for some time, but it eventually regenerates. Same situation if you kill the heart only.
She is a proper familiar of the spirit turtle. Even though I called the other things familiars, they are more like zombies loyal to a summoner rather than a familiar. She has her own will that is somewhat independent of the Spirit Turtle. You can kill her, but it won't affect the turtle.