Supercritical Carbon Dioxide (SC-CO₂) hydro-jet fracturing can increase gas production and reduce carbon dioxide emission, and is considered as a promising alternative for shale gas exploration. SC-CO₂ hydro-jet fracturing technology has resulted in multi-fracture network in the YanChang Well of Ordos Basin, China. However, the mechanism of SC-CO₂ hydro-jet fracturing is still not clear. To address the problem, experiments and specimens were designed based on Orthogonal Experimental Design (OED) to investigate the influential factors, including jet pressure (P_in), jet distance (S), nozzle diameter (d_n), perforation length (L) and perforation diameter (d_perf). In addition, the evaluation indexes, ambient pressure and the fracture profile were deeply discussed. The investigation results indicated that crack initiation on the root of perforation was prevented by the higher SC-CO₂ jet pressure. Particularly, when the nozzle diameter was more than the inlet diameter of casing (3 mm), the crack number on perforation dropped sharply. When the optimal perforation length and perforation diameter were respectively 50 mm and 6 mm, the peak values of the crack number and distribution range were observed. The results of Analysis of Variance (ANOVA) demonstrated that jet pressure and perforation length were the main influential parameters. With the increase in ambient pressure, the threshold pressure of fracture initiation increased. Three patterns of crack extension directions were found in the experimental specimens: surface fracture, longitudinal fracture, and transverse fracture.