  Given that the two-Higgs-doublet model of type III (2HDM-III) has the
potential to address the $R_{D^{(\ast)}}$ anomalies while the resolution to the
$R_{K^{(\ast)}}$ deficits requires new degrees of freedom within this
framework, we consider in this paper a unified scenario where the low-scale
type-I seesaw mechanism is embedded into the 2HDM-III, so as to accommodate the
$R_{D^{(\ast)}}$ and $R_{K^{(\ast)}}$ anomalies as well as the neutrino mass.
We first revisit the $R_{D^{(\ast)}}$ anomalies and find that the current
world-averaged results can be addressed at $2\sigma$ level without violating
the bound from the branching ratio $\mathcal{B}(B_c^-\rightarrow \tau^-
\bar{\nu})\leqslant 30\%$. The scenario predicts two sub-eV neutrino masses
based on a decoupled heavy Majorana neutrino and two nearly degenerate Majorana
neutrinos with mass around the electroweak scale. For the $R_{K^{(\ast)}}$
anomalies, the same scenario can generate the required Wilson coefficients in
the direction $ C_{9 \mu}^{\rm NP}=-C_{10 \mu}^{\rm NP}<0$, with
$\mathcal{O}(1)$ Yukawa couplings for the muon and the top quark.
