As a continuation of our previous work, we investigate the weak decays of doubly-heavy baryons $Xi_{QQ^{prime}}$ into sextet $Sigma_{Q^{prime}}$ with light-cone sum rules. We calculate the form factors for these decays with the parallel light-cone distribution amplitudes of $Sigma_{Q^{prime}}$. Numerical results of these form factors are used to predict the decay widths and branching ratios of the corresponding semi-leptonic processes. Parametric uncertainties and theoretical analyses are also given in detail. We find that the decay widths of $Xi_{cc}$ and $Xi_{bc}$ decays are several orders of magnitude larger than those of $Xi_{bb}$ decays.
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