The recent experimental results including R_{K^{(*)}}, R_{D^{(*)}}, (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^{(*)}} and R_{D^{(*)}} anomalies simultaneously when considering nonzero lambda '_{1jk}. For nonzero lambda '_{2jk}, this model fulfills the whole brightarrow sell ^+ell ^- fit but cannot be accordant with R_{D^{(*)}} 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.