Remote controllability, real-time response, and small size are critically requirement of medical devices operated in blind, unstructured, and fluidic environments of biomedical regions. Untethered swimming soft milli-robots have been developed to fulfill treatment and therapy in such that region under magnetic navigation. The soft robot's motor-less mechanism with a high-DOF utilizes magnetic compliance of the deformable structure with a minimal control of oscillating magnetic field. Theoretically, magnetic property of the robots is defined by magnetic moments consisting of orientation and strength. Orientation can be programmed by magnetizing technique, and strength is defined by quantity of magnetic moments in the structure. Herein, this work investigates how orientation and quantity of magnetic moments affect swimming behavior and performance of the robots. The soft robots are designed into three distinguish types of magnetic property embedded in the deformable structure; the I-robot has non-uniform magnetic orientation and uniform magnetic strength, the II-robot has uniform magnetic orientation and non-uniform magnetic strength, and the III-robot has non-uniform magnetic orientation and non-uniform magnetic strength. The results interestingly report that each type of robot's property functions mechanism and benefits swimming performance differently under the same control parameters. The I-robot does not have any exceptional potential, but the II-robot can be operated at the higher control frequency even reaching the step-out point. The III-robot shows the greatest performance in swimming and maneuverability. These results are useful to design a swimming soft-robot capable of applying for various purposes, especially when the demand concerns non-harm, small-scale, soft-interface, and remote controllability.