Your point about the bleeding is, as I said, well taken. You may be right about that and it seems hard to explain other than she just died of asphyxation FIRST. As for the grammar, I'm no expert but it appears to me that he is saying that the cause of death was... two things - asphyxia and craniocerebral trauma. He could have said it in reverse and got the same meaning; i.e. cause of death was ... craniocerebral trauma associated with asphyxation. The sentence just doesn't distinguish the two in terms of precedence as I read it.
BTW, welcome to FR.
If it was both, a conjuction would be used not a preposition. Cause of death is asphyxiation and cranial trauma.
Because of the lack of bleeding, it cannot be shown that she was struck first before being strangled, she was struck while being strangled at or very near the point of death and possibly even after death. There is plenty of evidence of asphyxiation from the petechial hemorrhage noted in the autopsy.