Columnar jointed basalt is a composite rock mass consisting of many prismatic rock blocks with irregular polygons in the transverse section. Similar material was used to simulate a columnar jointed rock mass with different dip angles (β = 0°–90°), and uniaxial compression, triaxial compression and true triaxial unloading tests were conducted to determine the anisotropic properties, and unloading failure mechanism of jointed basalt rock. The results show that the dip angle has significant effects on the strength anisotropy of the columnar jointed rock mass. The stress–strain curves under uniaxial and true triaxial unloading indicate strain softening, and the stress–strain curves under triaxial compression reflect strain hardening. The specimen with β = 60°–75° has the lowest strength and is most sensitive to the confining pressure. The analysis of the failure mode and failure mechanism of the columnar jointed rock mass under different load conditions indicate that the failure mode can be divided into three types: stress-controlled failure, structure-controlled failure, and stress-structure-controlled failure. The peak stress growth coefficient is higher under triaxial compression than under true triaxial unloading. Finally, the applicability of different strength criteria to the columnar jointed rock mass is analyzed by evaluating the fitting accuracy and comparing the test results with measured data. Regression analysis demonstrates that the Mogi-Coulomb strength criterion is better suited to the study data than the Drucker-Prager strength criterion. The research results have reference significance for the stability analysis of excavated tunnels in columnar jointed rock masses.