Three-dimensional printing with cement-based materials is a promising manufacturing technique for civil engineering applications that already allows for the design and the construction of complex and highly customized structures using a layer-by-layer deposition approach. The extrusion mechanism is one of the most expensive parts of the 3D printer. Also, for low-scale 3D printers, based on the shape of the extruder and the geometry limitation of the mixing blade, the 3D mixture is often limited to a narrow range of materials due to the risk of layer splitting or blockage. Therefore, there is a need to develop affordable and feasible alternatives to the current design–fabrication–application approach of 3D printers. In this paper, various newly designed mixtures of fiber-reinforced mortars that can be 3D printed using only a commercially available screw pump are analyzed based on their fresh properties and mechanical characteristics. The results, in terms of extrudability, buildability, flowability, and flexural and compressive strengths, highlight the potential of using this technology for constructing complex structures with high strength and durability. Also, the reduced facility requirements of this approach enable 3D printing to be made more available for civil engineering applications. With further innovations to come in the future, this method and these mixtures can be extended for the sustainable and economically feasible printing of single-family housing units.