Porphyry copper deposits (PCDs) occur in accretionary and collisional orogens, yet it is unclear how continental collision controls their formation. Two fundamental issues are debated: Which mechanism triggers melting of collision-thickened lithosphere, and which sources supply metals and volatiles necessary for formation of collision-related PCDs? Here, we image the lithospheric architecture of the Himalayan-Tibetan orogen that hosts abundant Miocene giant to large PCDs in Tibet, using joint inversion of surface wave and satellite gravity data, integrated with magnetotelluric (MT) array data and geochemical data. Our results show that the subducted Indian continental lithosphere was torn into several pieces with different subduction angles during the Cenozoic Indo-Asia collision. The tears in the Indian slab provides channels for asthenospheric upwelling, which reworks the overlying Asian lithosphere and triggers melting. This process generates ultrapotassic mafic melts that ascend and pond at the base of the crust, leading to high heat flow and supply of released H₂O for water-fluxed melting of the overlying thick crust and generation of hydrous granitoid magmas. Sulfide break-down in a juvenile Cu-rich lower-crustal source during melting increases the fertility of the granitoid magmas. Our study indicates that three key factors generate the collision-related PCDs: A torn slab subducted at moderate angle, prior fertilization of the lower crust with Cu, and trans-lithospheric vertical structures for magma ascent. Block margins in collisional orogens built above fossil oceanic subduction zones are optimal locations for the formation of giant PCDs. Therefore, regional-scale Nd-Hf-O isotopic mapping integrated with multiple geophysical inversions are key to mineral exploration for PCDs in collision systems.