  We theoretically demonstrate that class-I topological Dirac semimetals
(TDSMs) can provide a platform for realizing both electrically and magnetically
tunable spin-charge conversion. With time-reversal symmetry, the spin component
along the uniaxial rotation axis ($z$-axis) is approximately conserved, which
leads to an anisotropic spin Hall effect -- the resulting spin Hall current
relies on the relative orientation between the external electric field and the
$z$-axis. The application of a magnetic field, on the other hand, breaks
time-reversal symmetry, driving the TDSM into a Weyl semimetal phase and,
consequently, partially converting the spin current to a charge Hall current.
Using the Kubo formulas, we numerically evaluate the spin and charge Hall
conductivities based on a low-energy TDSM Hamiltonian together with the Zeeman
coupling. Besides the conventional tensor element of the spin Hall conductivity
$\sigma_{xy}^z$, we find that unconventional components, such as
$\sigma_{xy}^x$ and $\sigma_{xy}^y$, also exist and vary as the magnetic field
is rotated. Likewise, the charge Hall conductivity also exhibits appreciable
tunability upon variation of the magnetic field. We show that such tunability
-- as well as large spin-charge conversion efficiency -- arises from the
interplay of symmetry and band topology of the TDSMs.
