Low critical charge-current density and low energy dissipation are highly desired in magnetic random-access memories, requiring spin sources to exhibit both high charge-to-spin conversion efficiency (CSE) and high charge conductivity. Altermagnets with vanishing net magnetic moment and spin-splitting bands provide promising spin-source candidates for spin-splitting-torque magnetic random-access memories. However, achieving both high CSE and charge conductivity remains challenging in altermagnets. In this work, we introduce Dirac cones into two-dimensional d-wave altermagnets, where their intrinsically high carrier mobility enables tunable charge and spin conductivities with high CSE. Dirac-cone anisotropy provides an effective means of enhancing both CSE and charge conductivity, with cone tilting serving as an additional degree of tunability. Guided by this design principle, we identify a maximum CSE of 92% in Cr2SeTeS. When the Fermi level moves slightly away from the Dirac point, high CSE, high charge conductivity, and the resulting high spin conductivity can be simultaneously achieved. Our study advances the understanding of time-reversal-odd spin transport via Dirac-cone engineering and provides a practical route toward developing spin-source materials that combine high charge conductivity with highly efficient charge-to-spin conversion.