The $\ensuremath{\beta}$-decay half-lives of $^{128--130}\mathrm{Cd}$ have been measured with the newly commissioned GRIFFIN $\ensuremath{\gamma}$-ray spectrometer at the TRIUMF-ISAC facility. The time structures of the most intense $\ensuremath{\gamma}$ rays emitted following the $\ensuremath{\beta}$ decay were used to determine the half-lives of $^{128}\mathrm{Cd}$ and $^{130}\mathrm{Cd}$ to be ${T}_{1/2}=246.2\phantom{\rule{0.16em}{0ex}}(21)$ ms and ${T}_{1/2}=126\phantom{\rule{0.16em}{0ex}}(4)$ ms, respectively. The half-lives of the $3/{2}^{+}$ and $11/{2}^{\ensuremath{-}}$ states of $^{129}\mathrm{Cd}$ were measured to be ${T}_{1/2}(3/{2}^{+})=157\phantom{\rule{0.16em}{0ex}}(8)$ ms and ${T}_{1/2}(11/{2}^{\ensuremath{-}})=147\phantom{\rule{0.16em}{0ex}}(3)$ ms. The half-lives of the Cd isotopes around the $N=82$ shell closure are an important ingredient in astrophysical simulations to derive the magnitude of the second $r$-process abundance peak in the $A\ensuremath{\sim}130$ region. Our new results are compared with recent literature values and theoretical calculations.