The mass and coupling of the scalar tetraquark T-bb;(u) over bar(d) over bar(-) (hereafter T-b:(d) over bar(-)) are calculated in the context of the QCD two-point sum rule method. In computations we take into account effects of various quark, gluon and mixed condensates up to dimension ten. The result obtained for the mass of this state m = (10135 +/- 240) MeV demonstrates that it is stable against the strong and electromagnetic decays. We also explore the dominant semileptonic T-b:(d) over bar(-) -> (Z) over tilde (0)(bc;(u) over bar(d) over bar)l (nu) over bar (l) and nonleptonic decays T-b:(d) over bar(-) -> (Z) over tilde M-0(bc;(u) over bar(d) over bar), where (Z) over tilde (0)(bc;(u) over bar(d) over bar) is the scalar tetraquark composed of color-sextet diquark and antidiquark, and M is one of the final-state pseudoscalar mesons pi(-), K-, D- and D-s(-), respectively. The partial widths of these processes are calculated in terms of the weak form factors G(1(2))(q(2)), which are determined from the QCD three-point sum rules. Predictions for the mass, full width Gamma(full) = (10.88 +/- 1.88) x 10(-10) MeV, and mean lifetime tau = 0.61(-0.09)(+0.13) ps of the T-b:(d) over bar(-) obtained in the present work can be used in theoretical and experimental studies of this exotic state.