Insects and animals in nature generally have powerful muscles to guarantee their complex motion, such as crawling, running, and jumping. It is challenging for insect-sized robots to achieve controlled crawling and jumping within the scale of millimeters and milligrams. This article proposes a novelty bionic muscle actuator, where an electrical pulse is applied to generate joule heat to expand the actuator's chamber. Under the restoring force of the spring element, the chamber contracts back to the initial state to finish a complete cycle. The actuator can obtain high-frequency vibration under the high-frequency electrical signal. We propose a microrobot based on the novelty actuator to achieve controlled crawling and jumping over the obstacle of the millimeter-sized robot. The robot is fabricated with two actuators as a crawling module and one actuator as a jumping module, with a mass of 52 mg, length of 9.3 mm, width of 9.1 mm, and height of 4 mm. The microrobot has a maximum crawling turning velocity of 0.73 rad/s, a maximum jump height of 42 mm (10.5 times body height), and a maximum jump velocity of 0.91 m/s. This study extends the potential for applying the novelty bionic-muscle actuator to the microrobot.