2D Slice from a 3D "cross section slice"

I'm trying to extract (at runtime, at any angle) just the slice from a 3D cross-section slice. For example, the cross section of a cube at an angle, produces a triangular slice.

I'm considering either using shaders or to just use very vertex-dense meshes.

Shaders: There are existing shaders that provide cross sections, but is it possible to get the slice from this?

Vertex-dense mesh: Vertices intersected by a plane - I guess this would also be limited by the discrete nature of even a dense mesh.