How is she getting on at school? Does she have a lot of friends? What are her teachers like?

The reason I ask is because it's not "uncommon" for someone to use someone they love as a buffer when things aren't going right.

It could well be something medical, but bullying (either by classmates or teachers) shouldn't be ruled out, in my opinion, or even child abuse by someone she knows, unless you know for certain this isn't happening. How is she getting on with her school work? Is she keeping up with it okay or having difficulties?

I think children's behaviour can be more than just medical sometimes. If something's gone on at school, then children can "release" themselves when they get home. Something might be making her unhappy at school. Where would she hear such things as kill you and slice you up? Is someone saying these things to her so she's switching them to you?

Just a thought. I was bullied at school and it did have an impact on me and two of my friends were abused, so I always have an open mind on those subjects.