Ice in atmospheric clouds undergoes complex physical processes, interacting especially with radiation, which leads to serious impacts on global climate. After their primary production, atmospheric ice crystals multiply extensively by secondary processes. Here, it is shown that a mostly overlooked process of mechanical breakup of ice particles by ice-ice collisions contributes to such observed multiplication. A regime for explosive multiplication is identified in its phase space of ice multiplication efficiency and number concentration of ice particles. Many natural mixed-phase clouds, if they have copious millimeter-sized graupel, fall into this explosive regime. The usual Hallett-Mossop (H-M) process of ice multiplication is shown to dominate the overall ice multiplication when active, as it starts sooner, compared to the breakup ice multiplication process. However, for deep clouds with a cold base temperature where the usual H-M process is inactive, the ice breakup mechanism should play a critical role. Supercooled rain, which may freeze to form graupel directly in only a few minutes, is shown to hasten such ice multiplication by mechanical breakup, with an ice enhancement ratio exceeding 10(4) approximately 20 min after small graupel first appear. The ascent-dependent onset of subsaturation with respect to liquid water during explosive ice multiplication is predicted to determine the eventual ice concentrations.