Observations highlight the complex tectonic, magmatic, and geodynamic phases of the Cenozoic post-collisional evolution of the Himalayan-Tibetan orogen and show that these phases migrate erratically among terranes accreted to Asia prior to the Indian collision. This behavior contrasts sharply with the expected evolution of large, hot orogens formed by collision of lithospheres with laterally uniform properties. Motivated by this problem, we use two-dimensional numerical geodynamical model experiments to show that the enigmatic behavior of the Himalayan-Tibetan orogeny can result from crust-mantle decoupling, transport of crust relative to the mantle lithosphere, and diverse styles of lithospheric mantle delamination, which emerge self-consistently as phases in the evolution of the system. These model styles are explained by contrasting inherited mantle lithosphere properties of the Asian upper-plate accreted terranes. Deformation and lithospheric delamination preferentially localize in terranes with the most dense and weak mantle lithosphere, first in the Qiangtang and then in the Lhasa mantle lithospheres. The model results are shown to be consistent with 11 observed complexities in the evolution of the Himalayan-Tibetan orogen. The broad implication is that all large orogens containing previously accreted terranes are expected to have an idiosyncratic evolution determined by the properties of these terranes, and will be shown to deviate from predictions of uniform lithosphere models.