Modular manipulators have broad application prospects in the field of narrow confined space owing to their characteristics of superior dexterity. However, compared with traditional ones, their mechanism design, modeling, and inverse kinematics (IK) are challenging due to their special structures and redundant degrees-of-freedom. In this paper, a modular cable-driven manipulator (CDM) is designed. A lightweight and expandable structure is proposed to reduce weight of the whole manipulator and improve its environmental adaptability. To calibrate its global posture, angle sensors are equipped with its joints. Its kinematics are rigorously analyzed. To obtain the IK of a hyper-redundant CDM in real-time, a fast heuristic method with adaptive joint constraints is introduced. Then, a segmented IK strategy is proposed by extending the IK solver to local CDM, which realizes the local joint migration motion under the stable overall configuration. Finally, numerical simulations are conducted and a physical prototype is developed to carry out experiments. The results show that the designed CDM has great performance in dexterity and accuracy.