In the quark-diagram scheme, we study the charmed baryon decays of mathbf{B}_crightarrow mathbf{B}^* M, where mathbf{B}_c is Lambda _c^+ or Xi _c^{+(0)}, together with mathbf{B}^* (M) the decuplet baryon (pseudoscalar meson). It is found that only two W-exchange processes are allowed to contribute to mathbf{B}_crightarrow mathbf{B}^* M. Particularly, we predict {mathcal {B}}(Lambda _c^+ rightarrow Sigma ^{*0(+)} pi ^{+(0)})=(2.8pm 0.4)times 10^{-3}, which respects the isospin symmetry. Besides, we take into account the SU(3) flavor symmetry breaking, in order to explain the observation of {mathcal {B}}(Lambda _c^+rightarrow Sigma ^{*+}eta ). For the decays involving Delta ^{++}(uuu), we predict {mathcal {B}}(Lambda _c^+rightarrow Delta ^{++} pi ^-,Xi _c^+ rightarrow Delta ^{++} K^-) =(7.0pm 1.4,13.5pm 2.7)times 10^{-4} as the largest branching fractions in the singly Cabibbo-suppressed Lambda _c^+,Xi _c^+rightarrow mathbf{B}^*M decay channels, respectively, which are accessible to the LHCb, BELLEII and BESIII experiments.