As an emerging magnetic phase, altermagnets (AMs) with collinear compensated magnetism in real space and alternating spin splitting in the band structure have attracted widespread attention. Here, based on first-principles calculations, we demonstrate that the layer stacking imposes symmetry constraints on the spin and valley degrees of freedom (DOFs) in bilayer systems composed of two tetragonal altermagnetic monolayers, thereby enabling the tuning of these DOFs through interlayer sliding as well as by an external electric field. Using several representative AM systems, we reveal that the $\left[C_2\left|\right|\mathcal{P}\right]$ and $\left[C_2\left|\right|{\mathcal{M}}_{\mathcal{z}}\right]$ symmetries intrinsically enforce spin degeneracy, while the coupling between spin and layer DOFs enables spin-state tuning through the relative alignment (parallel or antiparallel) of the Néel orders in the two monolayers or by an external electric field. Appropriate interlayer sliding breaks the $\left[C_2\left|\right|{\mathcal{M}}_d\right]$ symmetry, thereby giving rise to valley splitting. Depending on whether these symmetries are preserved, stacking configurations generated by interlayer sliding can be classified into distinct magnetic states, enabling a unified description of spin and valley behaviors. Owing to the stacking-dependent spin and valley splitting, enhanced tunneling magnetoresistance can be realized in AM systems. This work highlights the intrinsic correlation among spin, valley, and layer DOFs, offering symmetry-based design principles for layer-based spintronic and valleytronic devices.

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• Crystal symmetry
• Spin polarization
• Valley degrees of freedom
• 2-dimensional systems
• Altermagnets
• Density functional calculations