Microgrippers that incorporate soft actuators are appropriate for micromanipulation or microsurgery owing to their ability to grasp objects without causing damage. However, developing a microgripper with a large gripping range that can produce a large force with high speed remains challenging in soft actuation mechanisms. Herein, we introduce a compliant microgripper driven by a soft dielectric elastomer actuator (DEA) called a spiral flexure cone DEA (SFCDEA). The submillimeter-scale SFCDEA exhibited a controllable linear displacement over a high bandwidth and the capability of lifting 100.9 g, which was 670 times higher than its mass. Subsequently, we developed a compliant microgripper based on the SFCDEA using smart composite microstructure technology to fabricate three-dimensional gripper linkages. We demonstrated that the microgripper was able to grasp various millimeter-scale objects with different shapes, sizes, and weights without a complex feedback control owing to its compliance. We proved the versatility of our gripper in robotic manipulation by demonstrating adaptive grasping and releasing of small objects using vibrations owing to its high bandwidth.