Fused deposition modeling (FDM) is one of the most widely deployed additive manufacturing methods, and the mechanical performance of FDM-printed parts is governed by a small set of strongly coupled process parameters. Silk PLA, a PLA-based filament engineered to deliver a high-gloss finish with improved mechanical performance, has received far less attention than commodity PLA, and its parameter–property relationships remain incompletely characterized. In this work, the effects of three FDM printing parameters: (i) layer height (0.10, 0.15, and 0.20 mm), (ii) extrusion temperature (200, 210, and 220 °C), and (iii) print speed (100, 120, and 140 mm/s) on the tensile characteristic of Silk PLA were investigated through a full-factorial design consisting of 27 parameter combinations and 135 ASTM D638 Type-I specimens. Tensile tests were performed on an MTS E42 universal testing frame, while Digital Image Correlation (DIC) was employed to obtain full-field longitudinal and transverse strain distributions and to identify the onset and location of necking. Analysis of variance (ANOVA) was used to assess the statistical significance, while an interpretable machine learning (ML) pipeline combining extreme gradient boosting (XGBoost), Shapley additive explanations (SHAP) values, and partial dependence plots (PDPs) was employed to quantify the relative influence of each parameter and elucidate its effect on the tensile response. Both analyses identified extrusion temperature as the dominant factor governing ultimate tensile strength and Young’s modulus. Partial dependence analysis further revealed that strength gains saturate above 210 °C and are maximized at an intermediate print speed of 120 mm/s, providing actionable guidance for process optimization. The highest tensile strength, 40.68 MPa, was achieved at a layer height of 0.20 mm, an extrusion temperature of 220 °C, and a print speed of 120 mm/s. DIC measurements showed that thinner layers (0.10 mm) produced higher breaking strains and necking that initiated at the gauge-section edges, whereas thicker layers (0.20 mm) shifted necking toward the mid-gauge. Together, the experimental, statistical, and ML results provide a consistent, mechanistically interpretable framework for optimizing FDM process parameters for Silk PLA functional parts.