  In this paper, we have examined the Sharma-Mittal holographic dark energy
model (SMHDE) in the framework of an isotropic and spatially homogeneous flat
Friedmann-Robertson-Walker(FRW) Universe by considering different values of
parameter $\delta$ and $R$, where the infrared cut-off is taken care by the
Hubble horizon. We examined the SMHDE model through the analysis of Statefinder
hierarchy and the growth rate of perturbation. The evolutionary trajectories of
the statefinder hierarchy $S_3^1$, $S_3^2$ $S_4^1$, $S_4^2$ versus redshift z,
show satisfactory behavior throughout the Universe evaluation. One promising
tool for investigating the dark energy models is the composite null
diagnostic(CND) $\{ S_3^1 - \epsilon\}$, where the evolutionary trajectories of
the $S_3^1 - \epsilon$ pair present different property and the departure from
$\Lambda$CDM could be well evaluated. Additionally, we investigated the
dynamical analysis of the model by $\omega_{D}-\omega^{'}_{D}$ pair analysis.
