Magnetic miniature robots (MMRs) are mobile actuators that can exploit their size to non-invasively access highly confined, enclosed spaces. By leveraging on such unique abilities, MMRs have great prospects to transform robotics, biomedicine and materials science. As having high dexterity is critical for MMRs to enable their targeted applications, existing MMRs have developed numerous soft-bodied gaits to locomote in various environments. However, there exist two critical limitations that have severely restricted their dexterity: (i) MMRs capable of multimodal soft-bodied locomotion have only demonstrated five-degrees-of-freedom (five-DOF) motions because the sixth-DOF rotation about their net magnetic moment axis is uncontrollable; (ii) six-DOF MMRs have only realized one mode of soft-bodied, swimming locomotion. Here we propose a six-DOF MMR that can execute seven modes of soft-bodied locomotion and perform 3-dimensional pick-and-place operations. By optimizing its harmonic magnetization profile, our MMR can produce 1.41-63.9 folds larger sixth-DOF torque than existing MMRs with similar profiles, without compromising their traditional five-DOF actuation capabilities. The proposed MMR demonstrated unprecedented dexterity; it could jump through narrow slots to reach higher grounds; use precise orientation control to roll, two-anchor crawl and swim across tight openings with strict shape constraints; perform undulating crawling across three different planes in convoluted channels. Keywords: Magnetic materials; soft actuators; miniature robots; locomotion. Corresponding author(s) Email: [email protected]