Tetradymite-type topological insulator Sn-doped Bp 101S0.9Te2S (Sn-BSTS), with a surface state Dirac point energy well isolated from the bulk valence and conduction bands, is an ideal platform for studying the topological transport phenomena. Here, we present high-pressure transport studies on single-crystal Sn-BSTS, combined with Raman scattering and synchrotron x-ray diffraction measurements. Over the studied pressure range of 0.7-37.2 GPa, three critical pressure points can be observed: (i) At similar to 9 GPa, a pressure-induced topological insulator-to-metal transition is revealed due to closure of the bulk band gap, which is accompanied by changes in slope of the Raman frequencies and a minimum in da within the pristine rhombohedral structure (R-3m); (ii) at similar to 13 GPa, superconductivity is observed to emerge, along with the R-3m to a C2/c (monoclinic) structural transition; (iii) at similar to 24 GPa, the superconducting transition onset temperature T-c reaches a maximum of similar to 12K, accompanied by a second structural transition from the C2/c to a body-centered cubic Im -3m phase.