Reprogrammable magneto-responsive soft actuators capable of working in enclosed and confined spaces and adapting functions under changing situations are highly demanded for new-generation smart devices. Despite the promising prospect, the realization of versatile morphing modes (more than bending) and local magnetic control remains challenging but is crucial for further on-demand applications. Here, we address the challenges by maximizing the unexplored potential of magnetothermal responsiveness and covalent adaptable networks (CANs) in liquid crystalline elastomers (LCEs). Various magneto-actuated contraction-derived motions that were hard to achieve previously (e.g., bidirectional shrinkage and dynamic 3D patterns) can be attained, reprogrammed, and assembled seamlessly to endow functional diversity and complexity. By integration of LCEs with different magneto-responsive threshold values, local and sequential magnetic control is readily realized. Many magnetic actuation portfolios are performed by rationally imputing “logic switch” sequences. Meanwhile, our systems exhibit additional favorable performances including stepwise magnetic controllability, multiresponsiveness, self-healing, and remolding ability.