Edge cracking, a common issue encountered during the rolling of magnesium alloys, holds substantial importance in determining the success of subsequent finishing processes. It serves as a pivotal parameter for evaluating the formability of rolled plates. In this particular investigation, researchers concentrated on understanding the behavior of edge cracks within the solid solution magnesium alloy designated as Mg-10Gd-3Y-2Ag-0.4Zr (expressed in weight percentage as GWQ1032K). To support this analysis, one delved into the thermal rheological characteristics of the magnesium alloy and established a mathematical relationship connecting rheological stress, strain rate, and temperature. This served as the foundation for a constitutive model tailored to the alloy. Furthermore, practical rolling experiments were conducted to examine how reductions in thickness influenced the morphology of edge cracks in rolled plates. The study also explored shifts in stress–strain behavior and microstructural changes during the deformation process. The results highlighted the substantial impact of compression levels on the magnesium alloy’s anisotropic behavior, subsequently influencing the shape of the resultant plate and the stress–strain characteristics observed during deformation. Significantly, as the rolling reduction increased, a notable increase in heat generation due to the plastic deformation of the magnesium alloy plate was observed. This heightened heat played a key role in dynamic recrystallizationand and facilitating the formation of the brittle Mg5(RE, Ag) phase. Consequently, minimizing the generation of this brittle phase emerged as a critical factor in effectively managing and controlling edge cracks in the rolling process.