First-principles calculations reveal that the fcc-to-hcp pressure-induced transformation in solid xenon proceeds through two mechanisms between 5 and 70 GPa. The dynamics of the phase transition involves a sluggish stacking-disorder growth at lower pressures (path I) that changes to a path involving an orthorhombic distortion at higher pressures (path II). The switchover is governed by a delicate interplay of energetics (enthalpy of the system for the structural stability) and kinetics (energy barrier for the transition). The two types of martensitic transformations involved in this pressure-induced structural transformation are a twinned martensitic transition at lower pressures and a slipped martensitic transition at higher pressures.