The Boolean functions for mesh manipulation that you find in a full 3D program are not built into Photoshop.
You should use a full 3D program such as Blender (free) to build the mesh
Alternatively if the cube cuts the cylinder exactly by 50% then you could try and create it in two parts. A half cylinder from a path extrusion, along with a full cylinder extrusion. Then merge them onto a single 3D layer, position them one on top of the other and group the objects.
Thanks a lot! I think I will go with the Blender solution.