The continuous development and utilization of underground space has led to an increasing number of short-distance constructions between new and existing tunnels. New tunnel construction affects the surrounding strata and destroys the structure and operation of the adjacent existing tunnel. Therefore, investigating the influence of new tunnels on the deformation of existing tunnels is crucial. Four centrifugal model tests simulating tunnel excavation processes were conducted to study the influence of tunnel excavation with different spacings on existing tunnels. Liquid was drained one section at a time to simulate the formation loss ratio produced by tunnel excavation and unloading during centrifuge operation, which eliminated the error caused by centrifuge shutdown–restart. Test results indicated that new tunnel excavation led to uneven settlement of the existing tunnel, and the settlement of the existing tunnel was greater than that of the two sides. Under the same burying condition of the new tunnel, the smaller the net distance between the new and existing tunnels, the greater the influence on the vertical and horizontal displacement of the existing tunnel, and the smaller the settlement of the ground surface. New tunnel excavation caused tensile stress near the excavation surface of the existing tunnel. A smaller clear distance resulted in a higher tensile stress. The centrifugal model tests provide technical support for tunnel construction and underground space development.