Vitrimers are functional cross-linked materials, exhibiting reprocessability, recyclability, and healability, and thus these are expected for application as sustainable materials. The functionalities of vitrimers are attributable to their associative bond exchange mechanism that is activated at a certain high temperature. The construction of a tuning method for the bond exchange properties must be useful for coming practical application of the vitrimer concept. Here, we prepare transesterification-based vitrimers via the thiol−epoxy click reaction to elucidate the essential effects of the branch numbers (f) at the cross-link point on their bond exchange properties, where f can be readily tuned via the functionality of the starting materials. The temperature-ramp creep and stress−relaxation tests then demonstrate that the vitrimer properties, such as the softening and stress−relaxation behaviors, vary depending on f. The experimental results derive some empirical relationships between f and the relaxation time and between f and activation energy of the bond exchange. In addition, the relaxation behavior of the vitrimer network with mixed f is investigated in the final section, showing the relaxation rate can be determined by the harmonic mean of relaxation time weighted by the mole fraction of the network components having different f. Overall, this study demonstrates that the design of a proper f is crucial to obtain the desired properties of vitrimers.