Due to the frequent occurrence of geological disasters, such as geological faults, tectonic activities, and local activities, the study of a cable structure capable of resisting large deformations and of absorbing energy is investigated. The plane length is increased step by step based on the deformation and energy absorption values of the original NPR anchor cable model. Three kinds of two-stage constant resistance bodies are designed following the three principles: first-stage friction plus second-stage expansion, primary expansion plus secondary expansion, and first-stage expansion plus second-stage friction. Moreover, a giant NPR anchor cable with extraordinary mechanical properties is developed. Via a theoretical analysis and laboratory static tensile tests on traditional NPR and giant NPR anchor cables, their force characteristics, constant resistance, and fluctuation trends are related to the size and the structure of the constant resistance body. In addition, the most remarkable improvement takes place in the cables’ deformation and energy absorption properties. The deformation increases from 1000–2000 mm to 3000–4000 mm, while the energy absorption value increases from 4.21 × 105–1.09 × 106 J to 3.2 × 106 J. The constant resistance value is also effectively enhanced to 550–723.7 kN. This provides a reliable technical support for their application in deep geological faults.