Altermagnets enable spin-split bands and anomalous transport phenomena with vanishing net magnetization, yet the symmetry-governed dependence of their optical and spin transport responses on the Néel-vector orientation remains largely unexplored. Using first-principles calculations and systematic magnetic point group analysis, we establish the complete response tensor forms dictated by the magnetic point group for the typical altermagnet CrSb, revealing a fundamental dichotomy: first-order Kerr/Faraday effects, governed by the antisymmetric optical conductivity, are odd functions of the Néel vector, while second-order Voigt/Schäfer-Hubert effects, determined by diagonal dielectric anisotropies, are even functions. Quantitatively, the Kerr rotation angle reaches up to $\sim 0.55\mathrm{mrad}$, the Faraday rotation up to $\sim 6.9\times {10}^5\mathrm{mrad}/\mathrm{cm}$, and the Voigt rotation up to $\sim {10}^6\mathrm{mrad}/\mathrm{cm}$, with their angular dependencies following distinct symmetry patterns. For the spin Hall effect, the time-reversal-odd ($\mathcal{T}$-odd) and time-reversal-even ($\mathcal{T}$-even) contributions to the spin Hall conductivity coexist and are of comparable magnitude ($\sim {10}^2\frac{\hslash }{e}\frac{\mathrm{S}}{\mathrm{cm}}$). In the ground-state Néel configuration along the $c$ axis, the $\mathcal{T}$-even spin Hall conductivity reaches $265\frac{\hslash }{e}\frac{\mathrm{S}}{\mathrm{cm}}$, while the $\mathcal{T}$-odd component is $85\frac{\hslash }{e}\frac{\mathrm{S}}{\mathrm{cm}}$, corresponding to charge-to-spin conversion efficiencies of 1.63% and 0.52%, respectively. Notably, reorienting the Néel vector not only modulates the transverse spin Hall components but also activates longitudinal spin-current–charge-current configurations (e.g., ${\sigma }_{xx}^{S_z}$ and ${\sigma }_{yy}^{S_z}$ for $\mathit{N}\left|\right|\frac{1}{2}\mathit{a}+\mathit{b}$), which are strictly forbidden in the conventional spin Hall effect. These results establish a comprehensive, symmetry-governed framework for the Néel-vector dependence of magneto-optical and spin-transport responses in CrSb, offering a multidimensional response spectrum for probing the Néel vector direction.

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• Magneto-optics
• Spin Hall effect
• Spintronics
• Altermagnets
• First-principles calculations