Bone tissue engineering (BTE) holds promise for treating bone defects, and 3D-printed porous scaffolds are pivotal for tissue regeneration. This study explores the impact of material extrusion 3D printing (ME3DP) process parameters (i.e., layer height and extrusion temperature) on 3D-printed porous scaffolds made of polyetherimide (PEI) material for BTE. The intricate relationships shaping scaffold dimensional accuracy, residual stresses, and warpage tendencies were unveiled using comprehensive numerical simulations. Our findings reveal that higher layer heights enhance dimensional stability, especially at lower printing temperatures, reducing maximum displacements. Consequently, lower layer heights lead to higher warpage critical values. This insight is instrumental in optimizing the material extrusion 3D printing (ME3DP) process, vital for precise net shape in BTE applications. Furthermore, residual stresses also revealed a correlation between higher printing temperatures and increased residual stresses. These findings emphasize the necessity of balancing material flow, printing temperature, and layer height for scaffold quality. Therefore, the right balance between precision and mechanical stability is critical for producing high-quality scaffolds that meet BTE requirements.