The accurate shape-sensing capability of the continuum mechanism is fundamental to improve and guarantee the motion control accuracy and safety of continuum surgical robots. This paper presents a data-based shape self-sensing method for a cable-driven notched continuum mechanism using its multidimensional intrinsic force information, which mainly includes the multidimensional forces/torques and driving cable tensions. The nonlinear hysteresis compensation and the shape estimation of the notched continuum mechanism play significant roles in its motion control. Calibration compensation of the notched continuum mechanism is performed based on kinematic modeling to improve the accuracy of its preliminary motion control. The hysteresis characteristics of the continuum mechanism are analyzed, modeled, and compensated through considering the abundant dynamic motion experiments, such that a feedforward hysteresis compensation controller is designed to improve the tracking control performance of the continuum mechanism. Based on the kinematic calibration and hysteresis compensation, combined with the motor displacement, driving cable tensions, and six-dimensional forces/torques information of the continuum mechanism, a data-based shape self-sensing method based on particle swarm optimization back propagation neural network (PSO-BPNN) is proposed in this study. Experimental results show that this method can effectively estimate the loaded and unloaded shape of the notched continuum mechanism, which provides a new approach for the shape reconstruction of cable-driven notched continuum surgical robots.