  The cutoff dependence of the Casimir energy and stress is studied using the
Green's function method for a system that is piecewise-smoothly inhomogeneous
along one dimension. The asymptotic cylinder kernel expansions of the energy
and stress are obtained, with some extra cutoff terms that are induced by the
inhomogeneity. Introducing interfaces to the system one by one shows how those
cutoff terms emerge and illuminates their physical interpretations. Based on
that, we propose a subtraction scheme to address the problem of the remaining
cutoff dependence in the Casimir stress in an inhomogeneous medium, and show
that the nontouching Casimir force between two separated bodies is cutoff
independent. The cancellation of the electric and magnetic contributions to the
surface divergence near a perfectly conducting wall is found to be incomplete
in the case of inhomogeneity.
