  We present effective field theories for the weakly coupled
Weyl-$\mathrm{Z}_2$ semimetal, as well as the holographic realization for the
strongly coupled case. In both cases, the anomalous systems have both the
chiral anomaly and the $\mathrm{Z}_2$ anomaly and possess topological quantum
phase transitions from the Weyl-$\mathrm{Z}_2$ semimetal phases to partly or
fully topological trivial phases. We find that the topological phase transition
is characterized by the anomalous transport parameters, i.e. the anomalous Hall
conductivity and the $\mathrm{Z}_2$ anomalous Hall conductivity. These two
parameters are nonzero at the Weyl-$\mathrm{Z}_2$ semimetal phase and vanish at
the topologically trivial phases. In the holographic case, the different
behavior between the two anomalous transport coefficients is discussed. Our
work reveals the novel phase structure of strongly interacting
Weyl-$\mathrm{Z}_2$ semimetal with two pairs of nodes.
