Let's say I have a head object and a sword object. I move the sword so that it is placed through the head. The part of the sword that is sticking out of the other side of the head I want to delete. The rest of the sword, including that part inside the head and the contact points between sword and head inside, I want to keep. How do I do that?
using the "difference" operation, wherever the sword object intersects the cube object, its volume is excluded.
The surface of the volume you subtract from the sword can be as complex as you need; you could use the head object, for example. Be careful though because the boolean modifier is computationally expensive and prone to error. Stick to simple, unsbdivided manifold meshes with only one part to them for the best chance of success.