Soft swimming microrobots have attracted considerable attention due to their potential applications in diverse fields ranging from biomedicines to environmental remediation. The locomotion control is of importance to the research of micromachines and microrobots. Inspired by the motility strategies of living microorganisms, such as flagella, cilia, and euglenoids, we focus on propulsion mechanisms with a design of Janus magnetoelastic crystalline membrane microswimmers actuated by time-varying magnetic fields. Such a Janus swimmer consists of a ferromagnetic cap completed by a magnetoelastic membrane body, where superparamagnetic particles are uniformly distributed on the surface. Under the influence of external magnetic fields, the swimmer undergoes complex shape transitions due to the interplay between the magnetic dipole-dipole interactions, the elasticity of the magnetoelastic membranes, and also the hydrodynamics of surrounding fluids. We show that those shape changes are nonreciprocal, which can generate locomotion such that the propulsion speed can be optimized by tailoring the membrane elastic properties. Besides, we also demonstrate that the Janus swimmer can be magnetically guided in a spiral trajectory. With such adequate control of locomotion in both speed and direction via non-invasive magnetic fields, this study provides another promising candidate design for the future development of microswimmers.