In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on a Markov-chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from Planck, baryon acoustic oscillation, and type-Ia supernovae; the dynamic measurement is $f{\ensuremath{\sigma}}_{8}(z)$ data points, which is obtained from the growth rate via redshift space distortion, and ${\ensuremath{\sigma}}_{8}(z)$ is the root-mean-square amplitude of the density contrast $\ensuremath{\delta}$ at the comoving $8{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ scale. The jointed constraint shows that $\ensuremath{\alpha}=0.00066{2}_{\ensuremath{-}0.000662}^{+0.000173}$ and ${\ensuremath{\alpha}}_{8}=0.82{4}_{\ensuremath{-}0.0166}^{+0.0128}$. The CMB and matter power spectra are both similar for the case of $\ensuremath{\alpha}=\text{mean}$ value and that of $\ensuremath{\alpha}=0$. However, the evolutionary curves of $f{\ensuremath{\sigma}}_{8}(z)$ are different. This means that, to some extent, the data points of the growth rate could break the degeneracy of the dark energy models.