Additive manufacturing of porous materials with a specific macrostructure and tunable mechanical properties is a state-of-the-art area of material science. Additive technologies are widely used in industry due to numerous advantages, including automation, reproducibility, and freedom of design. Selective laser melting (SLM) is one of the advanced techniques among 3D fabrication methods. It is widely used to produce various medical implants and devices including stents. It should be noticed that there is a lack of information on its application in stent production. The paper presents the technological aspects of CoCr stent SLM fabrication, including design of stents and development of regimes for their manufacturing. Physical, chemical, and technological properties of CoCr powder were initially determined. Parametric design of mesh stent models was adopted. A two-stage approach was developed to ensure dimensional accuracy and quality of stents. The first stage involves a development of the single-track fusion process. The second stage includes the stent manufacturing according to determined technological regimes. The single-track fusion process was simulated to assign laser synthesis parameters for stent fabrication. Melting bath temperature and laser regimes providing such conditions were determined. Twenty-seven SLM manufacturing regimes were realized. Dependence of single-tracks width and height on the laser power, exposition time, and point distance was revealed. The qualitative characteristics of tracks imitating the geometry of the stent struts as well as favorable and unfavorable fusion regimes were determined. The results of surface roughness regulating of the stents’ structural elements by various methods were analyzed. Thus, this two-staged approach can be considered as a fundamental approach for CoCr stent SLM fabrication.