Tuned viscous mass damper (TVMD) was applied for vibration control of the adjacent buildings by interconnecting the sub-structures. The response mitigation performance of TVMD was investigated based on the simplified adjacent single degree of freedom (SDOF) systems. Based on the stochastic theory, mitigation ratios of each sub-structure and the overall performance index for whole adjacent structures were established by using the mean square displacement response (MSDR) in order to evaluate the response mitigation performance of TVMD. Parametric study was performed to reveal variations of the response mitigation performance under the influence of TVMD and sub-structures parameters. Numerical optimization procedure was proposed to determine the best response mitigation performance and optimal TVMD parameters. Furthermore, it was simplified into a graphical procedure for practical design. Proposed design methods were illustrated with examples, and the simplified graphical procedure presented results with enough accuracy with reference to the numerical optimization procedure. The effectiveness of TVMD was verified through both frequency domain and time domain analysis. Compared with the conventional viscous damper, the TVMD optimized by the proposed design methods demonstrated significantly better energy dissipation and response mitigation performance at rather low demand of actual mass and damping coefficient. The energy dissipation enhancement owing to the tuning effect is achievable when the stiffness ratio of TVMD is within a proper range, which is lower than 0.1 in this study. By using the overall performance index, the sub-structure with a larger response can be rationally controlled with priority through the design methods.