This study experimentally characterized various green cementitious composites with inherent self-sensing capabilities for use in structural health monitoring. Four composite mortar mixes were prepared using different combinations of ordinary Portland cement, reactive magnesia, slag, and graphene oxide (GO), then cured in water (for cement mixes) or air (for magnesia–slag mixes). Compressive strengths were determined by testing 50 mm cubic specimens cured for 28 d, and electrical properties were determined over a broad alternating current frequency range (10 Hz to 100 kHz) using four probes embedded in prismatic specimens cured for 1–28 d or subjected to monotonic and cyclic loading after 28 d. The cement-based reference specimen exhibited the highest compressive strength (~56.9 MPa) at 28 d; the strength of the GO-modified cement specimen (CGS) was only slightly lower (52.3 MPa), indicating that the addition of GO had little effect on mechanical performance. By contrast, the magnesia–slag specimens exhibited lower strengths of 10.2 MPa (without GO) and 9.0 MPa (with GO). The four-probe measurements revealed that the incorporation of GO significantly reduced electrical resistance: the CGS specimen exhibited the lowest resistivity across all frequencies, approximately 30% and 250% lower than the resistivities of the cement and magnesia–slag specimens without GO, respectively. Notably, the CGS specimen also exhibited stable and repeatable piezoresistive responses under both monotonic and cyclic loading. These results confirm that GO-modified cementitious composites can simultaneously provide adequate structural capacity and reliable self-sensing functionality, thereby offering a promising solution for real-time structural health monitoring.