The weak decays of the axial-vector tetraquark $T_{bb;bar{u} bar{d}}^{-}$ to the scalar state $Z_{bc;bar{u} bar{d}}^{0}$ are investigated using the QCD three-point sum rule approach. In order to explore the process $T_{bb; bar{u} bar{d}}^{-} to Z_{bc;bar{u} bar{d}}^{0}l bar{ u_l}$, we recalculate the spectroscopic parameters of the tetraquark $T_{bb;bar{u} bar{d}}^{-}$ and find the mass and coupling of the scalar four-quark system $Z_{bc;bar{u} bar{d}}^{0}$, which are important ingredients of calculations. The spectroscopic parameters of these tetraquarks are computed in the framework of the QCD two-point sum rule method by taking into account various condensates up to dimension ten. The mass of the $T_{bb;bar{u} bar{ d}}^{-}$ state is found to be $m=(10035~pm 260)~mathrm{MeV}$, which demonstrates that it is stable against the strong and electromagnetic decays. The full width $Gamma$ and mean lifetime $tau$ of $T_{bb;bar{u} bar{d} }^{-}$ are evaluated using its semileptonic decay channels $T_{bb; bar{u} bar{d}}^{-} to Z_{bc;bar{u} bar{d}}^{0}l bar{ u_l}$, $l=e,mu$ and $tau$. The obtained results, $Gamma=(7.17pm 1.23)times 10^{-8 } mathrm{MeV}$ and $tau =9.18_{-1.34}^{+1.90}~mathrm{fs}$, can be useful for experimental investigations of the doubly-heavy tetraquarks.
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