Magnetic continuum robots (MCRs), which are free of complicated structural designs for transmission, can be miniaturized and are therefore widely used in the medical field. However, the deformation shapes of different segments, including deflection directions and curvatures, are difficult to control simultaneously under an external programmable magnetic field. This is because the latest MCRs have designs with an invariable magnetic moment combination or profile of one or more actuating units. Therefore, the limited dexterity of the deformation shape causes the existing MCRs to collide readily with their surroundings or makes them unable to approach difficult-to-reach regions. These prolonged collisions are unnecessary or even hazardous, especially for catheters or similar medical devices. In this study, a novel magnetic moment intraoperatively programmable continuum robot (MMPCR) is introduced. By applying the proposed magnetic moment programming method, the MMPCR can deform under three modalities, that is, J, C, and S shapes. Additionally, the deflection directions and curvatures of different segments in the MMPCR can be modulated as desired. Furthermore, the magnetic moment programming and MMPCR kinematics are modeled, numerically simulated, and experimentally validated. The experimental results exhibit a mean deflection angle error of 3.3° and correspond well with simulation results. Comparisons between navigation capacities of the MMPCR and MCR demonstrate that the MMPCR has a higher capacity for dexterous deformation.