  The anomalous spin Hall conductivity in the holographic model of Dirac
semimetals with two Dirac nodes protected by the crystal symmetry has been
elaborated. Such system besides the chiral anomaly possesses another anomaly
which is related to the $\mathbb{Z}_2$ topological charge of the system. The
holographic model of the system contains matter action with two $U(1)$-gauge
fields as well as the appropriate combination of the Chern-Simons gauge terms.
  We also allow for the coupling of two gauge fields {\it via} the kinetic
mixing parametrised by the coupling $\alpha$. The holographic approach in the
probe limit enables us to obtain Hall conductivity. The aim of this work is to
describe the phase transitions in the $\mathbb{Z}_2$ Dirac semimetals between
the topologically trivial and non-trivial phases. Interestingly the anomalous
Hall conductivity plays a role of the order parameter of this phase transition.
The holographically found prefactor of the Hall conductivity in the
topologically non-trivial phase, depends on the coupling $\alpha$ and the Chern
- Simons couplings.
