It might be balance as in keeping a long, heavy and weirdly weighted sword balanced so that the not only edge hits straight on but after the hit the sword doesn't tilt or fall ever so slightly to one side making the cut mostly a crush. An axe orients itself.
Momentum will keep the blade straight if it hits straight on, After cutting a bit into the flesh, it will self-stabilize due to the shape of the cut.
If you do not hit straight on (and the difference between "straight on" and "bad angle" can be really tiny.
That's why cutting water bottles or even paper is a decent way to practice cutting. If you hit a 0.5l bottle that's not rigidly attached to something, chances are, you'll just whack it away when you hit it with a bad angle.
A sheet of paper is even more of a bitch, since the cut has to be perfect, or else it'll just fold or get knocked away.
Though, when the sword is really heavy and the thing you wanna cut is fixed, it gets more "forgiving" of a bad angle.
Something that just came to my mind: Maybe it's an issue with the length of the sword, too. When the thing you wanna cut is below your waist, it starts getting hard to make a full cut. Imagine you hold the sword with both hands, trying to cut a melon on the ground, the angle between sword and ground will shape a triangle that prevents you from cutting all the way.
Maybe that's one of the things that happened there, too. The headman would strike your neck, cut into it, but the tip is stuck in the wooden block while the lower end of the blade only cut shallowly into the guys neck.
If I'm thinking of the one you are thinking about, urgh. I've heard from a teacher that pictures of the event were posted in Japanese newspapers. For those curious it happened during WW2 and the race was to see who could behead the most Chinamen so they had two rows of prisoner tied to poles iirc. It's possible it happened in Nanking but that's just a guess on my part.
I don't think there were photos of the dead people, but of the two soldiers and it was certainly published in a newspaper. Osaka Shimbun, if memory serves correctly.
Also, since this is kind of on topic of the whole beheading thing:
A few hundred years ago in Germany, there was an increasing number of people who'd kill someone and then go to the local sheriff to confess. This was the medieval version of the "cop assisted suicide", since killing yourself is the worst sin there is.
Unlike, say, murder, you can't confess and repent for committing suicide, since the sin is only completed when you die, therefore you can't confess and repent before that and you can't after for obvious reasons.
That's why a lot of suicidal people would kill someone else instead to get the death sentence, oftentimes they'd go for some really messed up shit, just to make sure they'll have their wish granted. This usually involved children or women. Really messed up shit.
So, when this trend started to become more and more numerous, the people in charge of the law acted against it:
When they suspected that someone had committed the crime purely to receive the death penalty, they'd grab those people, often remove their hair, teeth and nails, throw them into the deepest, dankest, coldest dungeon, have them eat literal filth and refuse them contact to the clergy, so they'd be unable to confess. Once every year, they'd be dragged through the streets to act as a living deterrent to anyone contemplating "suicide-by-cop".
Sometimes, I wonder if this wasn't also what we should be doing with IS terrorists.
