  The recent experimental results including $R_{K^{(\ast)}}$, $R_{D^{(\ast)}}$,
$(g-2)_\mu$ and $W$ mass show deviations from the standard model (SM)
predictions, implying the clues of new physics (NP). In this work, we
investigate the explanations of these anomalies in the $R$-parity violating
minimal supersymmetric standard model (RPV-MSSM) extended with the inverse
seesaw mechanism. The non-unitarity extent $\eta_{ee}$ and the loop corrections
from the interaction $\lambda'\hat L \hat Q \hat D$ are utilized to raise the
prediction of $W$ mass through muon decays. We also find that the interaction
$\lambda'\hat L \hat Q \hat D$ involved with right-handed (RH)/singlet
(s)neutrinos can explain the $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$ anomalies
simultaneously when considering nonzero $\lambda'_{1jk}$. For nonzero
$\lambda'_{2jk}$, this model fulfills the whole $b\to s\ell^+\ell^-$ fit but
cannot be accordant with $R_{D^{(\ast)}}$ measurements. The explanations in
both cases are also favored by $(g-2)_\mu$ data, neutrino oscillation data and
the relevant constraints we scrutinized. Furthermore, this model framework can
be tested in future experiments covering, e.g., the predicted lepton flavor
violations (LFV) at Belle II and the Future Circular Collider with $e^+e^-$
beams (FCC-ee), as well as the heavy neutrinos at future colliders.
