This paper presents a novel boundary collocation meshfree approach—space–time boundary moving least squares (BMLS) method to investigate the impact of transverse joints quality on the static and dynamic responses of a Xiaowan arch dam model. The proposed approach utilizes the space–time boundary moving least squares (BMLS) method based on one-dimensional moving least squares (MLS) technique to construct approximation formulas for solving three-dimensional elastic dynamic problems. Two models of Xiaowan arch dam, one with transverse joints and one without, were analyzed using the BMLS method to analyze the impact of transverse joint quality on the stability of the arch dam model. The numerical results suggest that the model with transverse joints already has good integrity when the ratio of the elastic modulus at the transverse joints to the elastic modulus of the dam material is 0.6. These findings demonstrate the promising development prospect of the BMLS method in practical engineering applications.