During excavation and unloading of underground chambers, the mechanical characteristics and crack propagation behavior of jointed rock formations are vital for project safety and stability. This study focuses on the jointed sandy slate in the underground powerhouse of the Kala Hydropower Station in Sichuan, and conducts series of tests on non-penetrating jointed sandy slate under triaxial loading and unloading conditions. We analyzed the mechanical properties and deformation characteristics under different stress paths, explored the applicability of various strength criteria, and investigated crack propagation mechanisms using fracture mechanics. It is found that: (1) As initial confining pressure increases, axial stress and strain at failure show an upward trend under different stress paths. (2) Compared to triaxial loading, unloading paths and jointed samples decrease load-bearing capacity. Unloading from axial stress to confining pressure increases cohesion by 4.1% and unloading from confining pressure to axial stress decreases it by 30.4%. The internal friction angle increases by 3.5% and 7.3% during axial compression, while jointed samples, compared with intact samples, show a decrease of 32.9% and 53% in cohesion and a decrease of 2.2% and 10% in internal friction angle respectively. (3) In terms of characterizing the strength properties of sandy slate throughout the loading and unloading processes, the Mogi-Coulomb strength criterion outperforms both the Mohr-Coulomb and Drucker-Prager criteria. (4) The theoretical critical angle increases with confining pressure, and biconjoint samples exhibit higher values than intact ones. The theoretical critical angles range from 55° to 60° under different loading paths.