Taking inspiration from nature, triply periodic minimal surfaces (TPMS) are tailored as a promising tool for designing internal pore architecture of porous biomaterials. In the next generation of scaffolds, meeting the conflicting biological and mechanical requirements is achieved by locally modulating biomechanical properties through a graded pore architecture design. To this, structure-property relationships have to be known for uniform scaffolds. In this study, numerical procedures were performed for a library of 240 TPMS-based unit cells (comprised of 10 volume fractions of 24 selected architectures) to explore the role of pore characteristics in determining normalized values stiffness, strength, and permeability. The associated design maps were developed based on which highly porous architectures with extreme properties were selected for experimental evaluations. Calcium sulfate scaffolds were designed based on the critical designs and 3D-printed (using a powder-based technique) in different cell sizes and size effects were addressed. The scaffolds were subjected to mechanical compression tests and the results were correlated with the computational data. Coupled experimental and numerical results suggest a great potential for TPMS-based architectures to be served in design and manufacturing of graded porosity/architecture scaffolds.