Additive manufacturing (AM) enables the fabrication of highly complex structures, which has led to its widespread adoption for producing parts designed via topology optimization. However, most topology optimization approaches overlook key AM-specific constraints, particularly the anisotropic strength that results from the layer-by-layer fabrication process. To address this gap, we present a stress-constrained topology optimization framework explicitly tailored for AM, which incorporates the anisotropic elastic and failure behavior of additively manufactured structures. Our formulation considers two anisotropic failure criteria—namely the Tsai-Wu and the Liu-Huang-Stout criteria—and provides vectorized expressions suitable for high-performance computing environments. We impose stress constraints locally at the centroid of each finite element and solve the locally constrained problem effectively via the augmented Lagrangian method. We demonstrate the effectiveness of the approach through numerical examples and experimental validation, showing that structures designed with our method consistently achieve their intended load-bearing capacities. Furthermore, we extend the framework to multi-material topology optimization by introducing a unified failure criterion capable of handling multiple material-specific failure criteria. Preliminary experiments show that our method reasonably predicts the structural behavior and failure thresholds of optimized multi-material components. This work advances the integration of topology optimization and additive manufacturing, providing a practical pathway toward the design of reliable, lightweight structures capable of withstanding mechanical loading without failing.