Millimeter-scale soft continuum robots offer safety and adaptability in transluminal procedures due to their passive compliance, but this feature necessitates interactions with surrounding lumina, leading to potential medical risks and restricted mobility. Here, we introduce a millimeter-scale continuum robot, enabling apical extension while maintaining structural stability. Utilizing phase transition components, the robot executes cycles of tip-based elongation, steered accurately through programmable magnetic fields. Each motion cycle features a solid-like backbone for stability, and a liquid-like component for advancement, thereby enabling autonomous shaping without reliance on environmental interactions. Together with clinical imaging technologies, we demonstrate the capability of navigating through tortuous and fragile lumina to transport microsurgical tools. Once it reaches larger anatomical spaces such as stomach, it can morph into functional 3D structures that serve as surgical tools or sensing units, overcoming the constraints of initially narrow pathways. By leveraging this design paradigm, we anticipate enhanced safety, multi-functionality, and cooperative capabilities among millimeter-scale continuum robots, opening new avenues for transluminal robotic surgery.