Tunneling stoppage often occurs during tunnel construction, especially in weak and rheological ground. The discontinuous excavation caused by the stoppage usually has a certain impact on the tunnel convergence and supporting pressure. This study develops a closed-form analytical solution for a deep-buried circular tunnel excavated in viscoelastic rock, in which the progress of longitudinal discontinuous excavation (the stoppage that occurs during tunneling) and the sequential installation of double elastic liners are considered. In the derivation, the change in the advance rate of the tunnel face before and after stopping is also considered. Corresponding to the whole construction process, the solution is solved step by step in five stages, and a generalized derivation procedure for any viscoelastic model is provided depending on the integral equation theory. Particularly for the Burgers model, explicit expressions for the time-dependent rock displacement and stress as well as the pressure on the two liners are presented, which can be reduced to the previous viscoelastic solutions with a constant advance rate or without the face effect. For validation purpose, comparisons are made between the proposed solution and previous existing solutions as well as the numerical results obtained by the finite-difference simulations. Additionally, to further verify the applicability of the presented solution in tunnel applications, the time-dependent tunnel convergence and liner stress of the four typical cross sections in the Saint Martin La Porte access adit are predicted, which are in good agreement with the corresponding field monitoring data. Compared with previous solutions, the proposed solution is more comprehensive and suitable for more complex tunnels with various excavation methods, rheological rocks, and supporting forms.