A new approach—radial Lorentz force augmented deep drawing—has been developed to enhance the material flow of the flange in an electromagnetically deep drawing process, by combining an additional radial inward Lorentz force at the periphery of the workpiece with an axial Lorentz force on the unsupported region of the workpiece. The radial and axial Lorentz forces are flexibly controlled using a dual-coil electromagnetic forming (EMF) system. In this paper, the flexibility of the proposed process on altering the deformation behavior of the workpiece is demonstrated, both experimentally and numerically. Twelve discharge voltage combinations for the two driving coils are designed to produce different Lorentz forces and induce different deformation behaviors. The morphology changes of the workpieces are measured to characterize the deformation behavior of the workpiece. It is found that the draw-in of the flange exponentially increases with the discharge voltage of the radial Lorentz force driving coil, while linearly increases with the discharge voltage of the axial Lorentz force driving coil. The improved draw-in effectively increases the forming height, changes the shape of the deformed workpiece from a cone to a cylinder, improves the fit between the workpiece and the die, and reduces the maximum thickness reduction from 25.6% to 6.7%. An electromagnetic-structure coupled model is developed to reproduce the experimental observations, and investigate the deformation mechanism of the process. The characteristics of the generated Lorentz forces explain the exponential dependencies of the draw-in on the discharge voltage of the radial Lorentz force driving coil. And the dynamic deformation histories of the workpiece reveal the mechanism of the improved draw-in driving the morphology changes of the formed workpiece. The study in this paper provides a better understanding of the deformation behavior of the proposed process, which is the fundamental for further developing of the process.