  We have investigated the Gamow-Teller transitions from ${}^{22}\textrm{Ne}$
to ${}^{22}\textrm{Na}$ by applying the isospin projected antisymmetrized
molecular dynamics combined with generator coordinate method. We have found
that the GT strength from $^AZ(J^\pi T)={}^{22}\textrm{Ne}(0_1^+1)$ is
fragmented into two final states ${}^{22}\textrm{Na}(1_{1,2}^+0)$, which belong
to $K=0$ and $K=1$ bands constructed by a prolately deformed $^{20}$Ne core
with a $S=1$ proton-neutron ($pn$) pair. Coupling of the intrinsic-spin of the
$pn$ pair with the core deformation play an important role in the GT
fragmentation. The symmetry breaking in the intrinsic-spin rotation leads to
the $SU(4)$-symmetry breaking of the $NN$ pair and causes the GT fragmentation.
We have compared the features of the GT transitions with those for
${}^{10}\textrm{Be}\to{}^{10}\textrm{B}$ and discuss the link of the
$SU(4)$-symmetry and the GT fragmentation in the deformed systems.
