When Orochimaru and the Third Hokage fight after the Chunin exam, the Third Hokage has the Shinigami cut out part of his soul, "taking away his jutsu" by making him lose the use of his arms. How does that work? Why does it specifically make his arms not work? Logically, it would pull from the part was the farthest from the chest where it was being pulled from, which would be the feet. Why is that not what happens?
I've just re-watched the scene in the anime where that happened, and it looked to me like the death god was clearly pulling on the part of Orochimaru's spirit that controls his arms(you can see hands at the end). That just happens to be where the death god was pulling on, and it happens to only have been pulled out to his elbows or so.
Maybe the 3rd drew the arms out on purpose because he deemed that to be the easiest or most effective thing to pull out first in-case he only had to partially do the job.
There's really not much more to it than that.
If you believe in how a soul works, then it's linked to all bodily functions.
If you were to lose the use of your legs, as long as your soul isn't damaged you can one day use your legs regardless. In Orochimaru's case, because Saratobi (the Third Hokage) was nearing death and was losing strength to even hold Orochimaru's soul, and that by even using the jutsu Saratobi had ended his own life; so, all Orochimaru needed to do was get free from his grasp to be the victor. Thus, he aimed for Orochimaru's arms as a means to stop him from ever using jutsu again, which would be a death sentence for him because it would mean that he could perform whatever jutsu he uses to change bodies
Thing is, Kabuto must have came up with something to allow Orochimaru to switch bodies and repair the damage to his soul, because even if there was another way for Orochimaru to jump bodies, the damage to his soul would have prevented him using his arms. I'm quite sure when he fights Naruto, and Naruto uses the Nine-Tails' Cloak, he's using his arms (though I could be mistaken, it's been a few months since I watched it).
As for how cutting a blob removes the use of his arms, Saratobi must have been able to "feel out" Orochimaru's arms and pull them out. In some anime and games, the soul has the same shape as the physical body with it being anchored to the head and feet so when you pull from the chest it kinda looks like you're pulling on a bow string. This could be similar; I just passed that part off as a Kage just being awesome to begin with.