When I would watch the Italian noni's using their mezzaluna they would turn the bowl with it as they worked. They never lifted it. And having a single large blade there was no need to clean it out between the blades. I will try to explain how she would turn the blade. I can picture it in my mind to this day.
If she was right handed she would come down a little harder with her right hand so that the 'knife' bit the bottom of the bowl and would turn it toward her. Sometimes she would rock the knife in a semi circle and then grab the bottom of the bowl and turn it. It all depended on her style. All the bowls had a little circle of minor cuts in the bottom. The bowls were made from very hard wood and could stand up to that knife grabbing it. Using that knife was a skill they developed as a child helping their mother.
Of course if she was left handed, reverse it.