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Composite asymmetric dark matter (ADM) is the framework that naturally explains the coincidence of the baryon density and the dark matter density of the Universe. Through a portal interaction sharing particle-antiparticle asymmetries in the Standard Model and dark sectors, dark matter particles, which are dark-sector counterparts of baryons, can decay into antineutrinos and dark-sector counterparts of mesons (dark mesons) or dark photon. Subsequent cascade decay of the dark mesons and the dark photon can also provide electromagnetic fluxes at late times of the Universe. The cosmic-ray constraints on the decaying dark matter with the mass of 1–10 GeV has not been well studied. We perform comprehensive studies on the decay of the composite ADM by combining the astrophysical constraints from $e^{\pm }$and $\gamma$ray. The constraints from cosmic-ray positron measurements by AMS-02 are the most stringent at $\gtrsim 2\mathrm{GeV}$: a lifetime should be larger than the order of ${10}^{26}\mathrm{s}$, corresponding to the cutoff scale of the portal interaction of about ${10}^8–{10}^9\mathrm{GeV}$. We also perform the dedicated analysis for the neutrino monoenergetic signals at Super-Kamiokande and Hyper-Kamiokande due to the atmospheric neutrino background in the energy range of our interest.