This paper presents experimental and numerical studies on the damage mode of the strand cables under explosions, followed by an assessment of the residual capacity of the blast-damaged cables. Field blast tests were carried out to obtain the damage profile and dynamic response of four strand cables considering different charge weights and standoff distances. The numerical model was established in LS-DYNA, in which the strands were innovatively simulated by the equivalent beam-shell model. The finite element model was then validated by the test results. The experiments revealed that the strand cable presented a whiplash motion under blast loading and the remaining force in the cable was proportional to the number of remaining strands. The damage of the strands can be classified into three levels according to the experimental observations, providing the basis for the prediction of its residual capacity. Based on the validated model, parametric studies were conducted to investigate the influence of prestressing force, cable dimension, charge weight, and standoff distance on the damage degree of strand cables. An empirical formula was then derived through multi-variable regression analysis, which could accurately predict the residual capacity of strand cables after explosions. The empirical formula can be used for the preliminary blast-resistant design of strand cables, emergency disposal of blast-damaged cables, and also provides a reference for the risk assessment of cable-stayed structures.