The construction of intersection tunnels in urban induces multiple stress redistribution in the surrounding rock, leading to engineering disasters such as instability in rock strata during excavation, disturbance of supporting structures in existing tunnels, and subsidence of ground adjacent buildings. Employing an appropriate construction method is crucial in circumventing excessive stress concentrations and large-scale rock strata subsidence, making it a key aspect of urban intersection tunnel engineering. In this paper, a numerical model for an urban intersection tunnel is developed based on an underground circular road project in a central business district. We conduct numerical simulations of the excavation processes using the full-section method, step method, and center cross diagram (CRD) method, respectively. The findings indicate that while different construction methods do not change the variation trends of surrounding rock stress and displacement, adjacent ground building deformation, and existing tunnel convergence, they affect the variation degrees. The maximum compressive and tensile stresses in the surrounding rock caused by the CRD method are the smallest, which are 3.56 MPa and 0.76 MPa, respectively. The maximum arch subsidence affected the amount, and horizontal convergence affected the amount of branch tunnel #1 caused by the CRD method are the smallest too, which respectively are 1.428 mm and 0.931 mm. The foundation subsidence and overall inclination of the ground building resulting from the three methods are identical. Then, we discuss the construction safety of the three methods and obtain the influence order on construction stability, which is as follows: full-section method > step method > CRD method. It is concluded that the CRD method is the most suitable for urban intersection tunnel engineering in terms of safety. This study could offer valuable insights for selecting construction methods in urban intersection tunnel engineering and provide a foundation for evaluating the safety and stability of tunnel construction.