  We demonstrate that it is possible to efficiently control ultracold chemical
reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers
in their metastable triplet states by choosing the internal hyperfine and
rovibrational states of the reactants as well as by inducing magnetic Feshbach
resonances with an external magnetic field. We base these conclusions on
coupled-channel statistical calculations that include the effects of hyperfine
contact and magnetic-field-induced Zeeman interactions on ultracold chemical
reactions of hyperfine-resolved ground-state Na and the triplet
NaLi(a$^3\Sigma^+$) producing singlet Na$_2$($^1\Sigma^+_g$) and a Li atom. We
find that the reaction rates are sensitive to the initial hyperfine states of
the reactants. The chemical reaction of fully spin-polarized, high-spin states
of rotationless NaLi(a$^3\Sigma^+, v = 0, N = 0$) molecules with fully
spin-polarized Na is suppressed by a factor of 10-100 compared to that of
unpolarized reactants. We interpret these findings within the adiabatic state
model, which treats the reaction as a sequence of nonadiabatic transitions
between the initial non-reactive high-spin state and the final low-spin states
of the reaction complex. In addition, we show that magnetic Feshbach resonances
can similarly change reaction rate coefficients by several orders of magnitude.
Some of these resonances are due to resonant trimer bound states dissociating
to the $N=2$ rotational state of NaLi(a$^3\Sigma^+, v = 0$) and would thus
exist in systems without hyperfine interactions.
