In order to investigate the law of the dynamic responses of a coupled tunnel with a large span and a small clear distance induced by the blasting load applied on the excavation face of the new horizontal adit for vehicles, a dynamic 3D finite element model was established based on the blasting excavation project of Yonghe tunnel’s new transverse passage in Guangzhou, China. The laws of the induced vibration velocity and dynamic stress of the existing tunnel are systematically analyzed according to the numerical calculation results. The results show that the main affected area of the existing lining is the lower arch waist facing the blast, where both the maximum vibration velocity and the maximum tensile stress appear. The horizontally radial vibration velocity (along the axis of the transverse passage) is the main contributor in the resulting vibration velocity of the lining. The distributed law and varying trend of the dynamic stress of the lining are similar to the vibration velocity, and there appears to be a satisfied positive linear correlation between the two indexes. When the distance from the excavation face of the horizontal adit to the existing tunnel is 10 m, the blasting-load-induced maximal vibration velocity and dynamic tensile stress of the tunnel are only 2.96 cm/s and 0.20 MPa, respectively, which are far less than that stipulated by the related technical code. A negative power exponential relationship between the peak vibration velocity of the existing tunnel lining and the distance from the excavation face of the transverse passage to the tunnel was also found. According to this relationship, the induced vibration velocity will exceed the threshold stipulated by the standard, i.e., 8 cm/s, if the distance decreases to 5.9 m. To improve the safety redundancy of the construction, the threshold of the distance from the excavation face of the horizontal adit to the existing tunnel is suggested to be 10 m under the current construction scheme.