  Aiming on testing the $\Xi_c-\Xi_c'$ mixing, we study the decays of
$\Xi_{cc}\to \Xi_c \pi$ with $\Xi_{cc} = (\Xi_{cc}^{++} , \Xi_{cc} ^+ )$,
$\Xi_c = (\Xi_c^{(\prime)+},\Xi_c^{(\prime)0})$ and $\pi = (\pi^+ , \pi^0)$.
The soft-meson limit is considered along with the pole model, and the baryon
matrix elements are evaluated by the bag model with and without removing the
center-of-mass motion (CMM). We find that the four-quark operator matrix
elements are about twice larger once the unwanted CMM is removed. We obtain
that ${\cal R} = {\cal B}(\Xi_{cc}^+ \to \Xi_c^{\prime +} \pi^+ )/ {\cal
B}(\Xi_{cc}^+ \to \Xi_c^{ +} \pi^+ ) = 0.87^{+0.17}_{-0.11} $ and $1.45$ with
and without removing the CMM, where the former is close to the lower bound and
the later is well consistent with ${\cal R} = 1.41 \pm 0.17 \pm 0.10$ measured
at LHCb. In addition, we show that after including the mixing, the up-down
asymmetry of $\alpha( \Xi_{cc}^+ \to \Xi_c^{(\prime)0 } \pi^+)$ flips sign.
Explicitly, we obtain that $\alpha(\Xi_{cc}^{+} \to \Xi_c^{\prime +} \pi^0) =
0.52$ and $\alpha(\Xi_{cc}^{+} \to \Xi_c^{ 0 } \pi^+) = 0.31$ with and without
the CMM corrections, respectively, which are all negative if the mixing is
absence. As a bonus, a positive value of $\alpha(\Xi_{cc}^{+} \to \Xi_c^{\prime
0} \pi^+)$ in experiments can also serve as the evidence of the $W$-exchange
contributions.
