Cable-driven serpentine manipulators (CSMs), due to their unique flexibility of movement, have broad application prospects in unstructured and confined environments. To enhance adaptability to different environments and tasks, the design of variable stiffness structures has long been a research focus for CSMs. Inspired by spatial folding mechanisms, such as umbrellas, we propose a novel variable-diameter-stiffness cable-driven serpentine manipulator (VDS-CSM). The standout feature of this innovation is its ability to achieve integrated control over both the outer diameter and the stiffness of the manipulator. First, we present the structural design of the novel VDS-CSM, whose outer diameter and stiffness can be continuously adjusted. Second, we establish the kinematics, statics, and stiffness models for VDS-CSM. Based on this, we conduct an in-depth study of the manipulator's stiffness characteristics. Simulation data indicate that the change ratio of the manipulator's end stiffness is approximately proportional to the square of the change ratio in the manipulator's outer diameter. Finally, we build a VDS-CSM experimental system. Through experiments, the accuracy of the proposed model for VDS-CSM is verified. The experimental results show that the outer diameter and stiffness of the manipulator can vary by 200% and 400%, respectively.