This study investigates the direct tensile mechanical behavior of cement mortar plates reinforced with a galvanized steel mesh and randomly incorporated alkali-resistant glass fibers. An experimental program was executed using direct tensile tests on thin mortar specimens containing fiber volumetric fractions of 0%, 4%, 6%, 8%, and 10% relative to the cement volume. To rigorously characterize the mechanical response, the study quantified the apparent initial stiffness, 0.2% offset stress, ultimate tensile strength, and post-offset energy absorption capacity. Results indicate that increasing alkali-resistant glass-fiber content systematically modified the global tensile response of the composite system. At 10% glass-fiber content, the mean crosshead-derived apparent initial tensile stiffness was 10.43 times that of the reference group without glass fibers. The characteristic stress determined using the adopted 0.2% offset criterion and the ultimate tensile strength increased by 154.5% and 74.1%, respectively, while the apparent post-offset energy absorption increased by 68.4%. Because strain was derived from crosshead displacement, the apparent stiffness and energy-absorption parameters represent the global specimen–grip–machine response rather than intrinsic material properties. The experimental results exhibited acceptable repeatability, although the apparent tensile stiffness showed greater variability than the strength-related parameters. These findings support the continued development of the investigated composite configuration for thin cementitious elements requiring improved tensile response and damage tolerance.