  We study exact Lagrangian fillings of Legendrian links of $D_n$-type in the
standard contact 3-sphere. The main result is the existence of a Lagrangian
filling, represented by a weave, such that any algebraic quiver mutation of the
associated intersection quiver can be realized as a geometric weave mutation.
The method of proof is via Legendrian weave calculus and a construction of
appropriate 1-cycles whose geometric intersections realize the required
algebraic intersection numbers. In particular, we show that in $D$-type, each
cluster chart of the moduli of microlocal rank-1 sheaves is induced by at least
one embedded exact Lagrangian filling. Hence, the Legendrian links of
$D_n$-type have at least as many Hamiltonian isotopy classes of Lagrangian
fillings as cluster seeds in the $D_n$-type cluster algebra, and their
geometric exchange graph for Lagrangian disk surgeries contains the cluster
exchange graph of $D_n$-type.
