Massive fluid injection can reactivate pre-existing faults or fractures and induce deformation as either seismic slip, slow slip or aseismic slip. These shear deformations, controlled by frictional strength and stability, may lead to different shear permeability evolutions. Previous studies have explored frictional stability-permeability relationships of carbonate-rich and phyllosilicate-rich samples during shear deformation, suggesting that phyllosilicate-rich shale has a lower frictional strength, but higher frictional stability and larger permeability reduction than that of carbonate-rich shale. This qualitative result is sufficient to identify the role of individual mineral group (i.e., tectosilicate, carbonate, and phyllosilicate) in prompting this response. Indeed, it is still uncertain whether or not a quantitative relationship of frictional stability-permeability relationships of fractures exists. In this study, we perform a series of hydroshearing experiments on saw-cut fractures of natural rocks (Green River shale, Opalinus shale, Longmaxi shale, Tournemire shale, Marcellus shale, and Newberry tuff) with distinct mineralogical compositions to understand the frictional stability-permeability relationships with respect to individual mineral groups. Our experimental results indicate that permeability change increases non-linearly with frictional strength while decreases non-linearly with frictional stability. These relationships imply that clay-rich fractures may be easily reactivated with aseismic deformation due to low frictional strength and high frictional stability, meanwhile, the permeability may decline due to clay swelling and wear product compaction. On the contrary, tectosilicate-rich fractures show the opposite trend. These results are significant for providing valuable references for understanding how permeability evolves in engineering activities like shale reservoir stimulation and CO2 caprock integrity evaluation.