  The combinatorial mutation $\mathrm{mut}_w(P,F)$ for a lattice polytope $P$
was introduced in the context of mirror symmetry for Fano manifolds in [1]. It
was also proved in [1] that for a lattice polytope $P \subseteq N_\mathbb{R}$
containing the origin in its interior, the polar duals $P^* \subseteq
M_\mathbb{R}$ and $\mathrm{mut}_w(P,F)^* \subseteq M_\mathbb{R}$ have the same
Ehrhart series. For extending this framework, in this paper, we introduce the
combinatorial mutation for the Minkowski sum of rational polytopes and rational
polyhedral pointed cones in $N_\mathbb{R}$. We can also introduce the
combinatorial mutation in the dual side $M_\mathbb{R}$, which we can apply for
every rational polytope in $M_\mathbb{R}$ containing the origin (not
necessarily in the interior). As an application of this extension of the
combinatorial mutation, we prove that the chain polytope of a poset $\Pi$ can
be obtained by a sequence of the combinatorial mutation in $M_\mathbb{R}$ from
the order polytope of $\Pi$. Namely, the order polytope and the chain polytope
of the same poset $\Pi$ are mutation-equivalent.
