Pneumatic micro-extrusion (PME) is a direct-write additive manufacturing process, which has emerged as a robust, high-resolution method for the fabrication of a broad spectrum of biological tissues and organs. PME allows for noncontact multimaterial deposition of functional inks for tissue engineering applications. In spite of the advantages and engendered potential applications, the PME process is inherently complex, governed not only by complex physical phenomena but also by material–process interactions. Consequently, investigation of the influence of PME process parameters as well as the underlying physical phenomena behind material transport and deposition in PME would be inevitably a need. The overarching goal of this research work is to fabricate biocompatible, porous bone tissue scaffolds for the treatment of osseous fractures, defects, and diseases. In pursuit of this goal, the objectives of the work are: (i) to investigate the influence of seven consequential scaffold design factors and PME process parameters on the mechanical properties of fabricated bone tissue scaffolds and (ii) to explore the underlying dynamics behind material transport in the PME process, using a three-dimensional computational fluid dynamics (CFD) model. To investigate the effects of the design and process parameters, a series of experiments were designed and conducted. Layer height was identified as the most significant factor in this study. An increase in the layer height led to less overlap between subsequent layers, which allowed for more shrinkage and ultimately a reduction in scaffold diameter. In addition, print speed appeared as an influential factor in this study. An increase in the print speed resulted in a decline in linear mass density and thus in the extent of fusion between subsequent deposited layers. Besides, it was observed that there was a strong correlation between deposition mass and compression modulus. Overall, the results of this study pave the way for future investigation of PME-deposited polycaprolactone (PCL) scaffolds with optimal functional and medical properties for incorporation of stem cells toward the treatment of osseous fractures and defects.