The stability of an arch dam can be significantly damaged by an extreme underwater explosion. This study proposed a damage index for assessing the degree of local damage of an arch dam after the dam was subjected to an underwater explosion. The damage index was applied to assess local damage at the middle part of the dam, surcharge holes, and abutment. A model was developed to evaluate the stability of the entire dam based on the spatial distribution of damage and the damage on the base interface. Results showed that local explosion damage at flood discharge holes or abutments might cause instability of the arch dam. When the contact explosion action location is on the abutment, it only needs 310 kg to cause the overall damage of the arch dam, while when the action location is on the middle part of the dam, the quantity of explosive required is 2800 kg.