In narrow, unstructured underwater environments such as environmental monitoring and minimally invasive medical procedures, micro soft robots exhibit unique advantages due to their flexible movement capabilities and small size. At the same time, applying bionic technology to the structural design of micro soft robots can significantly improve their swimming performance. However, limited by their miniaturization, these robots are difficult to power internally and usually adopt a wireless power supply method. This study designs and fabricates a magnetically responsive, cownose ray-inspired micro soft robot based on the swimming principle of the cownose ray. The robot is made of a certain proportion of NdFeB and PDMS. Then, a three-dimensional Helmholtz coil is used to generate an oscillating harmonic magnetic field to conduct swimming experiments on the robot, exploring the influence of magnetic field parameters on the robot's swimming performance. The experimental results show that the swimming speed is the fastest at B = 5 mT and f = 11 Hz, reaching 5.25 mm/s, which is about 0.5 body lengths per second. In addition, by adjusting the current direction and frequency of the coil, the robot can perform different swimming modes such as straight swimming, turning swimming, and directional swimming. By employing a stepwise adjustment method, the impact of response errors on the robot's trajectory can be effectively reduced. This study demonstrates a method for magnetically driven micro soft robots, laying a foundation for the application of wireless-driven robots in underwater narrow spaces.