Ternesite–ye’elimite (TCSA) cement is a new type of environmentally advantageous binder prepared by introducing ternesite, a reactive phase, into belite calcium sulfoaluminate cement clinker. This paper reports the laboratory production of TCSA cement by the addition of minor elements to achieve the coexistence of ternesite and ye’elimite. The influence of dopants on the mineralogical composition of clinkers and the clinkering conditions for the preparation of TCSA cement clinkers were investigated by X-ray powder diffraction and scanning electron microscopy. The mechanical properties and hydration products of the cement pastes were also studied. The results indicated that the addition of CaF2, P2O5 and Na2O can promote the coexistence of ternesite and ye’elimite, and that Na2O is the most effective candidate. TCSA cement clinkers could be successfully prepared at 1150 °C for 30 min by doping 0.3% Na2O. The TCSA cement clinkers exhibited shorter setting times than the BCSA cement clinkers. The later strength of TCSA cement showed a significant increase compared with BCSA cement. The effect of Na2O was different on the strength development for TCSA and BCSA cement. The dissolution of ternesite could promote the formation of ettringite. The reactivity of belite was higher in TCSA cement due to the formation of strätlingite.