We have measured the cross sections for $\pi^0\pi^\pm$ photoproduction on the nucleon in the deuteron with an electromagnetic calorimeter system, FOREST, at the Research Center for Electron Photon Science, Tohoku University, Japan. The incident photon energy ranges from 570 to 1150 MeV, corresponding to the $\gamma N$ center of mass, $W_{\gamma N}$, from 1400 to 1750 MeV. The baryon resonances coupling to $\rho^+ n$ and $\rho^-p$ are observed as intermediate states together with $\Delta$-Kroll-Ruderman background components. The angular distributions for the produced $\rho^+$ and $\rho^-$ mesons are convex downward and upward at high energies ($W_{\gamma N}\sim 1720$ MeV), respectively.