In order to explore the problems of load transfer and anchorage mechanisms of tensile anchors under pull-out load for geotechnical anchoring systems, a step-wise mathematical model is established which considers the linear–nonlinear shear stress and shear displacement of the anchorage segment, using an elasto-plastic constitutive model. The displacement, axial force, and shear stress of the anchorage interface in different stages (elastic, plastic, and debonding) are analyzed and solutions are derived. And the theoretical solutions for the ultimate pull-out load of the anchor at each stage are also presented. Two in situ pull-out tests are used to verify and apply these findings in engineering. The results show that the stepwise composite model could reflect the bonding, softening and residual characteristics of the anchoring interface. In the process of the pull-out load increasing, the pulling end of the anchor initially enters the plastic stage and the debonding stage, respectively, and the failure of the anchor occurs at the pulling end, and as the axial force transfers down deeper, the damage gradually spreads deeper. The axial force distribution of the anchorage section is a monotonically decreasing curve, and the peak point of the shear stress gradually moves deeper. The calculation results of the axial force distribution curve and load–displacement curve of the anchor are in good agreement with the measured values, which verifies the rationality and reliability of the theoretical prediction method. This method can provide a theoretical reference for the load transfer analysis and design of tension anchors for geotechnical anchoring systems.