Most untethered magnetic soft robots are controlled by a continuously applied magnetic field. The accuracy of their motion depends completely on the accuracy of external magnetic field, consequently any slight disturbance may cause a dramatic change. Here, we report a new structure and driven method design to achieve a novel magnetic soft robot, denoted as “BUCK”, which can achieve accurate and stable locomotion with weakly dependence on the magnetic field. The robot BUCK consists of functional magnetic composite materials with one central transportation platform and four crawling arms, whose motion is mainly based on hyperelastic buckling and recovering of the arms. BUCK is capable of cargo transportation with multimodal locomotion, such as crawling, climbing, and turning with high adaptability to various surfaces. Due to the applied discontinuous magnetic field, BUCK consumes much less driven energy compared with conventional magnetic robots. Moreover, we develop theoretical and numerical models to rationally design the precisely controlled BUCK. Our study shows applications in terms of transportation functions, such as for optical path adjustments and photographic tasks in complex circumstances. This work also provides new ideas on how to utilize nonlinear deformation more efficiently; one could combine the benefits for both the flexible electronics and actuation applications.