Al
The article says:
Judge Giles Forrester said: "The attack was vicious and cruel. Not only was she stabbed twice in the neck, she was indeed decapitated whilst alive."
I read this as saying that her head was cut off whilst she was still alive. The cutting will have taken a while, during which the poor victim is alive.
Obviously she died as soon as the main nerves in her spine and blood vessels were cut.
The article does not say that she stayed alive after the beheading.