  The semileptonic and nonleptonic decays of the double-beauty axial-vector
tetraquark $T_{bb;\overline{u} \overline{d}}^{-}$ to a state
$\widetilde{T}_{bc; \overline{u}\overline{d}}^{0}$ (hereafter $T_{bb}^{-}$ and
$\widetilde{T} _{bc}^{0}$, respectively) are investigated in the context of the
QCD sum rule method. The final-state tetraquark $\widetilde{T}_{bc}^{0}$ is
treated as an axial-vector particle built of a heavy axial-vector diquark $
b^{T}\gamma _{\mu }Cc$ and light scalar antidiquark $\overline{u}C\gamma_{5}
\overline{d}^{T}$. Its spectroscopic parameters are calculated using the
two-points sum rules by taking into account contributions of quark, gluon and
mixed condensates up to dimension $10$. We study the dominant semileptonic
$T_{bb}^{-} \to \widetilde{T}_{bc}^{0}l\overline{\nu }_{l}$ and nonleptonic
decays $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}M$, where $M$ is one of the
pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$. The partial widths
of these processes are computed in terms of weak form factors $G_{i}(q^2),\
i=1,2,3,4$, extracted by employing the QCD three-point sum rule approach.
Predictions obtained for partial widths of considered decays are used to
improve accuracy of theoretical predictions for full width and lifetime of the
tetraquark $T_{bb}^{-}$, which are important for experimental exploration of
this exotic meson.
