Scaffolds are of great importance in tissue engineering applications as they provide a mechanically supportive environment for cellular activity, which is particularly necessary for hard tissues such as bone. Notably, the mechanical properties of a scaffold vary with differing design parameters such as those related to scaffold height and internal structure. Thus, the present study aimed to explore the relationship between design parameters and mechanical properties of composite polycaprolactone (PCL) and nano-hydroxyapatite (nHAp) scaffolds fabricated by three-dimensional (3D) printing. We designed and printed scaffolds with different internal structures (lattice and staggered) and varying heights (4, 6, 8 and 10 layers), and consistent porosity (50%) for the purpose of comparison. Then, we examined the scaffold microstructure (pore size and penetration between layers) using scanning electron microscopy (SEM) and mechanical properties (elastic modulus and yield strength) using compressive testing. Our results illustrated that the microstructural parameters were related to scaffold design. At higher heights, pore size increased while penetration between layers decreased; thus, mechanical properties were affected. Results of mechanical testing demonstrated that for lattice scaffolds, elastic modulus was similar for 6 vs 4, and 8 vs 4 layers but ~33% lower for 10 layers vs 4 layers. Similarly, yield strength was comparable for 6 vs 4, and 8 vs 4 layers but ~27% lower for 10 layers vs 4 layers. With staggered scaffolds, when compared to 4-layer results, elastic modulus was similar for 6 layers but was ~43% lower for 8 layers and ~38% lower for 10 layers. Staggered scaffolds had ~38%, ~51%, and ~76% lower yield strength when the number of layers were increased from 4 to 6, 8, and 10 layers, respectively. When comparing lattice and staggered scaffolds with the same layer number, elastic modulus was similar, apart from 8-layer scaffolds where the staggered design was ~42% lower than lattice. Yield strength was similar between 4-layer staggered and lattice scaffolds, while staggered scaffolds with 6, 8, and 10 number of layers showed ~43%, ~45%, ~68% lower strength, respectively, than those found in lattice scaffolds with the same layer numbers. Mechanical properties of 3D printed scaffolds depended on scaffold height for both lattice and staggered internal structures. Staggered scaffolds had lower mechanical properties than the lattice scaffolds with the same height and were more sensitive to the change in scaffold height. Taken together, lattice scaffolds demonstrated the advantages of more stable mechanical properties over staggered scaffolds. Also, scaffolds with lower height were more promising in terms of mechanical properties compared to scaffolds with greater height.