Shape-programmable soft materials that exhibit integrated multifunctional shape manipulations, including reprogrammable, untethered, fast, and reversible shape transformation and locking, are highly desirable for a plethora of applications, including soft robotics, morphing structures, and biomedical devices. Despite recent progress, it remains challenging to achieve multiple shape manipulations in one material system. Here, we report a novel magnetic shape memory polymer composite to achieve this. The composite consists of two types of magnetic particles in an amorphous shape memory polymer matrix. The matrix softens via magnetic inductive heating of low-coercivity particles, and high-remanence particles with reprogrammable magnetization profiles drive the rapid and reversible shape change under actuation magnetic fields. Once cooled, the actuated shape can be locked. Additionally, varying the particle loadings for heating enables sequential actuation. The integrated multifunctional shape manipulations are further exploited for applications including soft magnetic grippers with large grabbing force, sequential logic for computing, and reconfigurable antennas. Keyword: shape memory polymers, soft active materials, magnetic soft material, soft robotics, soft material computing