The semileptonic decays of the lowest-lying double-heavy baryons are treated in a quark model. For the Ξbb, hyperfine mixing in the spin wave function leaves the total rate for decay into the lowest lying daughter baryons essentially unchanged, but changes the relative rates into the Ξbc and [Formula: see text]. The same pattern is obtained in the decays of the Ωbb. For the Ξbc, this mixing leads to factor of about 17 suppression in the decay rate to the [Formula: see text] when wave functions truncated to the largest components are used, but the total semileptonic decay rate of the parent baryon remains essentially unchanged. For the Ωbc, the decay to the [Formula: see text] is suppressed by a factor of more than 25 from the unmixed case. When the full wave functions are used, the large suppression of the decays to the [Formula: see text] and [Formula: see text] persists.