We study the semileptonic and non-leptonic charmed baryon decays with SU(3) flavor symmetry, where the charmed baryons can be Bc = (Ξc0, Ξc+, Λc+), Bc′ = (Σc(++,+,0), Ξc′ (+,0), Ωc0), Bcc = (Ξcc+ +, Ξcc+, Ωc+) or Bcc = Ωccc+ +. With Bn(′) denoted as the baryon octet (decuplet), we find that the Bc → Bn′ℓ+νℓ decays are forbidden, while the Ωc0 → Ω−ℓ+νℓ, Ωcc+ → Ωc0ℓ+νℓ, and Ωccc+ + → Ωcc+ℓ+νℓ decays are the only existing Cabibbo- allowed modes for Bc′ → Bn′ℓ+νℓ, Bcc → Bc′ℓ+νℓ, and Bccc → Bcc(′)ℓ+νℓ, respectively. We predict the rarely studied Bc → Bn(′)M decays, such as . For the observation, the doubly and triply charmed baryon decays of are the favored Cabibbo-allowed decays, which are accessible to the BESIII and LHCb experiments.