The growth of open-sea aquaculture has led to the development of advanced semi-submersible fish cages, such as Ocean Farm 1, Havfarm, and Shenlan 1. However, the net system is vulnerable to damage under rough sea conditions in open waters and requires continuous monitoring via load sensors. This study numerically investigates tendon failures in nets and the corresponding structural responses of a semi-submersible fish cage. The numerical method integrates a rigid body dynamics (RBD) model for simulating hull motions and a modified extended position-based dynamics (XPBD) method for modelling the deformations of mooring lines and nets connected to the hull. Hydrodynamic forces on the hull are calculated using a potential theory, while the Morison model is applied to evaluate drag forces on mooring lines and slender hull structures. The screen model is employed to compute hydrodynamic forces acting on the nets. Validation against experimental results confirms the accuracy of the method in predicting the natural periods of the fish cage. Results show that the mean tension in a broken tendon decreases significantly, by at least 38%. A strong correlation between the mean tension and the height of the breaking point is identified across various tendons and sea conditions. A tendon failure detection method is proposed to locate the broken tendon and determine the height of the breaking point. Additionally, the study captures the rapid tearing of nets following the rupture of a pre-tensioned tendon, resulting in a 5 m2 hole within 0.12 s. These numerical results provide critical insights into monitoring and maintaining the net systems of semi-submersible fish cages and advance offshore aquaculture engineering.