Spintronic materials with two-dimensional (2D) transition-metal dichalcogenide (TMD)/ferromagnet (FM) interfaces have received a great deal of interest recently due to strong modulation of the magnetic properties, which provide attractive opportunities for magnetic information storage. Here, we demonstrate the strong spin-orbit coupling (SOC) effect and great interfacial tuning of magnetization dynamics in $M{X}_{2}$/$\mathrm{Co}\text{\ensuremath{-}}\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}$ thin films by means of a time-resolved magneto-optical Kerr approach, where M is chosen as $\mathrm{Mo}$ or $\mathrm{W}$ and X is $\mathrm{S}$ or $\mathrm{Se}$. The significant drop of demagnetization time, ${\ensuremath{\tau}}_{m}$, and increase of magnetic damping factor, ${\ensuremath{\alpha}}_{s}$, clearly highlight the presence of high interfacial SOC strength in just one monolayer of ${\mathrm{Mo}\mathrm{S}}_{2}$. Compared with the single $\mathrm{Co}\text{\ensuremath{-}}\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}$ film, the precession frequency, f, is lowered after inserting a $M{X}_{2}$ layer, suggesting a reduction of the effective magnetization, $4\ensuremath{\pi}{M}_{\mathrm{eff}}$, originating from the interfacial d-d hybridization effect. The role of SOC strength on ${\ensuremath{\tau}}_{m}$, ${M}_{\mathrm{eff}}$, and ${\ensuremath{\alpha}}_{s}$ is confirmed by using different TMD materials, and thus, demonstrates that the element M plays a dominant role. The samples with ${\mathrm{WS}}_{2}$ or ${\mathrm{W}\mathrm{Se}}_{2}$ have much shorter ${\ensuremath{\tau}}_{m}$, smaller ${M}_{\mathrm{eff}}$, and larger ${\ensuremath{\alpha}}_{s}$ values due to the strong SOC interaction of heavier atoms. The observed efficient control of dynamic magnetic behavior will further promote the development of TMD/FM materials for practical spintronic applications with ultrafast manipulation speed and low energy consumption.