The cable-driven hyper-redundant manipulators (CDHRMs) are especially suitable for operations in the long narrow confined space due to their light-slender and superior dexterous bodies. However, the high redundancy also brings challenges to mechanical structure and kinematic planning. In this article, a highly compact coiled CDHRM (C-CDHRM) that mimics the coiling behavior of snakes is designed, including 12 fully-constrained rigid bodies, 36 double-screw retractors, and a coiled feeding mechanism that can coil or uncoil according to task needs. Corresponding to the characteristics of the C-CDHRM, a variable redundancy kinematic model (VRKM) is established, including the equivalent mapping from the planning point to the cable length and the analytical approximate workspace that can determine the minimum number of active segments according to the target. Based on the VRKM, multiconstraint kinematic planning (MCKP) is presented, which integrates the smoothness of cable-driven joints, the mobility of the feeding base, and the collision-free performance of complex environments. In simulation tests, the MCKP has a higher success rate, smoother angular distribution, and less motion than typical methods. Furthermore, the MCKP can continuously get joint configurations of reaching the target in dense obstacles. Finally, a prototype is developed and typical experiments are performed. The results show that the VRKM and MCKP enable the bioinspired coiled manipulator to exert excellent dexterity and maneuverability.