Soft magnetic composites are exceptional because they can be controlled remotely, move quickly, conform to hard things, and interact with people safely. However, even with all these features, magnetic elastomers suffer a lack of stability due to the high softness of the elastomer. This issue affects their controllability and repeatability. This article introduces a novel conceptual design of magneto‐responsive shape memory polyurethane (SMP) foam composites with high stability and reversibility. The fabrication technique is based on the silicone resins filled with strontium ferrite magnetic particles and a thin SMP foam placed onto one side. Material properties, room‐temperature shape recovery features, and magnetization conditions necessary for the process are determined by experimental studies of composite actuators. As a result, a workable, light, stable, soft composite gripper with programmable magnetic patterns is created, which can carry out activities like grabbing, holding, and moving objects in horizontal and vertical directions when a low magnetic field is applied. The SMP foam increases the contact surface and decreases the weight by up to three times providing better stability compared to the magnetic elastomer without SMP foam. The shape‐recoverable gripper with a small contract area can lift objects eight times heavier than its weight.