Over the past decade, 3D printing with concrete has been widely adopted worldwide. The primary drivers for this innovation are the reduction in manual labor and the more efficient use of natural resources. New materials that are suitable for 3D printing are developed, which are characterized by rapid setting and robust physical and mechanical properties. In this study, for the first time, ternary gypsum–cement–pozzolanic (GCP) composites were developed and evaluated for use in 3D printing. These composites are associated with durability in water as Portland cement (PC) while maintaining the rapid hardening properties of gypsum. Two types of secondary gypsum—recycled plasterboard gypsum (RG) and phosphogypsum (PG)—were used as the calcium hemihydrate component. The compressive strength test showed that 37 MPa can be achieved, which is comparable to that of traditional PC-based 3D printable mixtures. For the first time in a 3D print test, it was experimentally proved that GCP mixtures have good stability and buildability up to 35 layers. According to Life Cycle Analysis, elaborated material gives a carbon footprint reduction of up to 40%, compared to traditional PC mortar, thus supporting the sustainable use of this innovative composite.