Magnetic continuum robots (MCRs) have become popular owing to their inherent advantages of easy miniaturization without requiring complicated transmission structures. The evolution of MCRs, from initial designs with one embedded magnet to current designs with specific magnetization profile configurations (MPCs), has significantly enhanced their dexterity. While much progress has been achieved, the quantitative index-based evaluation of deformability for different MPCs, which can assist in designing MPCs with enhanced robot deformability, has not been addressed before. Here we use “deformability” to describe the capability for body deflection when an MCR forms different global shapes under an external magnetic field. Therefore, in this paper, we propose methodologies to design and control an MCR composed of modular axially magnetized segments. To guide robot MPC design, for the first time, we introduce a quantitative index-based evaluation strategy to analyze and optimize robot deformability. Additionally, a control framework with neural network-based controllers is developed to endow the robot with two control modes: the robot tip position and orientation ($M_{1}$) and the global shape ($M_{2}$). The excellent performance of the learnt controllers in terms of computation time and accuracy was validated via both simulation and experimental platforms. In the experimental results, the best closed-loop control performance metrics, indicated as the mean absolute errors, were 0.254 mm and 0.626$^\circ$for mode$M_{1}$and 1.564 mm and 0.086$^\circ$for mode$M_{2}$.