Auxetic structures, known for their unique mechanical properties, have gained significant attention across diverse fields. This study designs, manufactures, and optimizes bioinspired auxetic structures for biomedical applications, specifically bone and tendon tissue regeneration. A comparative analysis is conducted to evaluate the compressive and tensile properties of various auxetic designs. All structures are optimized using a cost‐effective methodology that integrates the finite element method with data‐driven supervised machine learning, maximizing Young's modulus with minimal porosity changes. The findings reveal that design variables significantly influence both auxeticity and mechanical properties. For instance, Young's modulus increases by 135.5% in sharp sinus (SS) and curved sinus (CS) structures while maintaining similar auxeticity. In contrast, the star (St) design shows a 76.5% increase in Young's modulus, with auxeticity increasing from −0.45 to −0.915. The modified re‐entrant ( M ‐Re) structure exhibits higher Poisson's ratio values, closely mimicking cancellous bone. Additionally, structures with higher auxeticity using re‐entrant (Re) designs prove suitable for tendon tissue engineering. SS, CS, and St structures offer versatility in achieving a diverse Young's modulus range, making them well‐suited for tendon tissue engineering alongside the Re structure.