When facing Sukkarak for the first time, Haru says "How many times do I have to hit him with this axe?" Seeing as Haru has a weapon that is distinct from what an axe whereas Sukkarak uses an axe, I believe we have a misunderstanding!
It's possible she was referring to him and his axe and in that case it's not really worth mentioning the axe and just becomes "How many more times do I have to hit him?"
You can also have "...with my sword?" or "...with this sword?" or even swap out sword for blade/edge/etc.