Measurements in the $b \to c {\tau}^- \bar{\nu}_{\tau}$ transitions suggest violation of lepton flavor universality (LFU). Assuming the flavor anomalies are due to new physics (NP) beyond the Standard Model (SM), we analyse the semileptonic decays of some heavy $b$-baryons to $c$-baryons, $\Sigma_b \to \Sigma_c {\tau}^- \bar{\nu}_{\tau}$ and $\Sigma_b \to \Sigma_{c}^* {\tau}^- \bar{\nu}_{\tau}$, which are mediated by $b \rightarrow c \tau^- \bar{\nu}_{\tau}$ transitions. Using a general effective Hamiltonian which includes both SM and NP contributions, we study and discuss the effects of the new contributions on the semileptonic $q^2$ spectra, such as the differential decay rate, ratio of branching fractions, forward-backward asymmetry of the charged lepton, convexity parameter and longitudinal polarization of the charged lepton in various new physics scenarios.