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I like the question and not to spoil to much of the story. Yes he can kill demons but since he wasn't born naturally with the ability to kill demons, it will take some time for him to properly manifest these powers but can still defeat them and banish them back to the Warp. Great question, if there are more let me know I would be happy to answer them.
The axe came into existence then, chopped off the demons head and basically disappeared. But it might appear again Khorne loves his champions, as much as a god of murder can.