The largest products of magmatic activity on Earth, the great bodies of granite and their corresponding large eruptions, have a dual nature: homogeneity at the large scale and spatial and temporal heterogeneity at the small scale(1-4). This duality calls for a mechanism that selectively removes the large-scale heterogeneities associated with the incremental assembly(4) of these magmatic systems and yet occurs rapidly despite crystal-rich, viscous conditions seemingly resistant to mixing(2,5). Here we show that a simple dynamic template can unify a wide range of apparently contradictory observations from both large plutonic bodies and volcanic systems by a mechanism of rapid remobilization (unzipping) of highly viscous crystal-rich mushes. We demonstrate that this remobilization can lead to rapid overturn and produce the observed juxtaposition of magmatic materials with very disparate ages and complex chemical zoning. What distinguishes our model is the recognition that the process has two stages. Initially, a stiff mushy magma is reheated from below, producing a reduction in crystallinity that leads to the growth of a subjacent buoyant mobile layer. When the thickening mobile layer becomes sufficiently buoyant, it penetrates the overlying viscous mushy magma. This second stage rapidly exports homogenized material from the lower mobile layer to the top of the system, and leads to partial overturn within the viscous mush itself as an additional mechanism of mixing. Model outputs illustrate that unzipping can rapidly produce large amounts of mobile magma available for eruption. The agreement between calculated and observed unzipping rates for historical eruptions at Pinatubo and at Montserrat demonstrates the general applicability of the model. This mechanism furthers our understanding of both the formation of periodically homogenized plutons (crust building) and of ignimbrites by large eruptions.