Emergent layered Cu-bearing van der Waals (vdW) compounds have great potentials for use in electrocatalysis, lithium batteries, and electronic and optoelectronic devices. However, many of their alluring properties such as potential superconductivity remain unknown. In this work, using CuP2Se as a model compound, we explored its electrical transport and structural evolution at pressures up to ∼60 GPa using both experimental determinations and ab initio calculations. We found that CuP2Se undergoes a semiconductor-to-metal transition at ∼20 GPa at room temperature and a metal-to-superconductor transition at 3.3-5.7 K in the pressure range from 27.0 to 61.4 GPa. At ∼10 and 20 GPa, there are two isostructural changes in the compound, corresponding to, respectively, the emergence of the interlayer coupling and start of interlayer atomic bonding. At a pressure between 35 and 40 GPa, the vdW layers start to slide and then merge, forming a new phase with high coordination numbers. We also found that the Bardeen-Cooper-Schrieffer (BCS) theory describes quite well the pressure dependence of the critical temperature despite occurrence of a possible medium-to-strong electron-phonon coupling, revealing the determinant roles of the enhanced bulk modulus and electron density of states at high pressure. Moreover, nanosizing of CuP2Se at high pressure further increased the critical temperature even at sizes approaching the Anderson limit. These findings would have important implications for developing novel applications of layered vdW compounds through simple pressure tuning of the interlayer coupling.