We extend the colored Zee-Babu model with a gauged \(U(1)_{B-L}\) symmetry and a scalar singlet dark matter (DM) candidate \(S\). The spontaneous breaking of \(U(1)_{B-L}\) leaves a residual \(Z_2\) symmetry that stabilizes the DM and generates tiny neutrino mass at the two-loop level with the color seesaw mechanism. After investigating dark matter and flavor phenomenology of this model systematically, we further focus on its imprint on two of cosmic-ray anomalies: the Fermi-LAT gamma-ray excess at the Galactic Center (GCE) and the PeV ultra-high energy (UHE) neutrino events at the IceCube. We found that the Fermi-LAT GCE spectrum can be well fitted by DM annihilation into a pair of on-shell singlet Higgs mediators while being compatible with the constraints from relic density, direct detections as well as dwarf spheroidal galaxies in the Milky Way. Although the UHE neutrino events at the IceCube could be accounted for by resonance production of a TeV-scale leptoquark, the relevant Yukawa couplings have been severely limited by current low energy flavor experiments. We then derive the IceCube limits on the Yukawa couplings by employing its latest 6-year data.