The dynamics of polymer nanocomposites (PNCs) are dictated by two intertwining components, the polymer matrix and the nanoparticle network, whose characteristics have not been elucidated. Here, we unravel the salient features of the polymer matrix dynamics and the nanoparticle network dynamics through dielectric spectroscopy and rheology. Dielectric measurements show that the dynamics of the polymer matrix of PNCs are almost identical to that of the neat polymer. In contrast, rheological measurements exhibit a strong deviation in the dynamics of PNCs from that of the neat polymer. Detailed analyses show that the rheology captures both contributions of the polymer matrix and the nanoparticle network while dielectric measurements are only sensitive to polymer matrix dynamics. Moreover, the dynamics of the polymer matrix and the nanoparticle network have very different temperature dependences, leading to a dynamic decoupling phenomenon and the breakdown of the time-temperature superposition principle in PNCs.