Polygonal models don't have an inside. They tell a renderer where their surfaces are.
If you want to slice an object as if it were solid, you have to reconstruct a surface where the slice cuts across it.
Here we have a cube inside a sphere inside a cube. All three objects have a Boolean modifier assigned to them.

The other cube displayed in wireframe to the left is a cutter object, and will be used as a target in the Boolean modifiers, set to 'Difference'. This will cut away the objects inside its volume, an construct a surface at its intersection with them, making it look as if the objects are solid.
Actually, there are 3 separate cutter-cubes, one as a target for each modifier, with their leading faces just slightly displaced from one another. If all the objects were cut in exactly the same place, Blender wouldn't know which new cut surface was in front of which, and there would be rendering artefacts. So the outside cube is cut away slightly more than the sphere, which is cut away slightly more than the inner cube.
Now if you animate the cutter-cubes together, you can create the illusion that the objects are solid.
