  We propose a new kind of CP violation effect -- the double-mixing CP
asymmetry -- in a type of cascade decays that involves at least two mixing
neutral mesons in the decay chain. It is induced by the interference between
different oscillation paths of the neutral mesons in the decay process. The
double-mixing CP asymmetry is of critical importance for phenomenology,
providing opportunities for clean determination of CKM phase angles free of
uncertainties induced by the strong dynamics. To illustrate this point, we
perform a phenomenological analysis on two examples: $B^0_s \to \rho^0 K \to
\rho^0 (\pi^-\ell^+{\nu}_\ell)$ and $B^0 \to D^0 {K} \to D^0
(\pi^+\ell^-\bar{\nu}_\ell)$. Our results demonstrate that the double-mixing CP
asymmetry can be numerically significant in the absence of strong phases, as
shown by the former example. Additionally, the latter example showcases the
direct extraction of weak and strong phases from data, without the need for
theoretical inputs.
