Photodisintegration of the deuteron into two $\Delta$-isobars at large center of mass angles is studied within the hard rescattering model (HRM). According to the HRM, the reaction proceeds in three main steps: the photon knocks the quark from one of the nucleons in the deuteron; the struck quark rescatters off a quark from the other nucleon sharing the high energy of the photon; then the energetic quarks recombine into two outgoing baryons emerging at large transverse momenta. Within the HRM, the cross section is expressed through the amplitude of $pn\rightarrow \Delta\Delta$ scattering which is evaluated based on the quark-interchange model of hard hadronic scattering. The resulting cross section of the deuteron breakup to $\Delta^{++}\Delta^{-}$ is noticeably larger than that of the breakup to the $ \Delta^{+}\Delta^{0}$ channel. Also, the angular distributions for these two channels are markedly different. These can be compared with the predictions based on the assumption that two hard $\Delta$-isobars are the result of the disintegration of initial $\Delta\Delta$ components of the deuteron wave function. In such cases, the angular distributions and cross sections of the breakup in both $ \Delta^{++}\Delta^{-}$ and $\Delta^{+}\Delta^{0}$ channels are expected to be similar.