This paper explores a multi-cell multiple-input single-output (MISO) downlink communication system enabled by a unique transmissive reconfigurable intelligent surface (TRIS) transceiver configuration. Within this system framework, we formulate an optimization problem for the purpose of maximizing the minimum rate of users for each cell via designing the transmit beamforming of the TRIS transceiver, subject to the power constraints of each TRIS transceiver unit. Since the objective function is non-differentiable, the max-min rate problem is difficult to solve. In order to tackle this challenging optimization problem, an efficient low-complexity optimization algorithm is developed. Specifically, the log-form rate function is transformed into a tractable form by employing the fractional programming (FP) methodology. Next, the max-min objective function can be approximated using a differentiable function derived from smooth approximation theory. Moreover, by applying the majorization-minimization (MM) technique and examining the optimality conditions, a solution is proposed that updates all variables analytically without relying on any numerical solvers. Numerical results are presented to demonstrate the convergence and effectiveness of the proposed low-complexity algorithm. Additionally, the algorithm can significantly reduce the computational complexity without performance loss. Furthermore, the simulation results illustrate the clear superiority of the deployment of the TRIS transceiver over the benchmark schemes.