Based on our understanding of the atomic mechanisms of melting in binary crystalline solid solutions, we propose a unified two-order-parameter mean-field model to describe solid-state amorphization under polymorphic constraints. In this framework, we treat both thermal melting and amorphization on equal footing as a topological-order-to-disorder transition. The primary order parameter is defined such that it represents the loss of the long-range order. The elastic strain field induced by composition disorder that plays an important role at low temperature is described by a bilinear coupling with the primary order parameter. We show that solid-state amorphization can be considered as an extension of a melting transition at low temperature under polymorphic constraints. This theory can also address endothermic melting as well as exothermic melting at low temperature. We present phase diagrams and the corresponding thermodynamic quantities for a model binary crystalline solution system at and near the transitions.