  The ground-state phases of anisotropic mixed diamond chains with spins 1 and
1/2 are investigated. Both single-site and exchange anisotropies are
considered. We find the phases consisting of an array of uncorrelated spin-1
clusters separated by singlet dimers. Except in the simplest case where the
cluster consists of a single $S=1$ spin, this type of ground state breaks the
translational symmetry spontaneously. Although the mechanism leading to this
type of ground state is the same as that in the isotropic case, it is
nonmagnetic or paramagnetic depending on the competition between two types of
anisotropy. We also find the N\'eel, period-doubled N\'eel, Haldane, and
large-$D$ phases, where the ground state is a single spin cluster of infinite
size equivalent to the spin-1 Heisenberg chain with alternating anisotropies.
The ground-state phase diagrams are determined for typical sets of parameters
by numerical analysis. In various limiting cases, the ground-state phase
diagrams are determined analytically. The low-temperature behaviors of magnetic
susceptibility and entropy are investigated to distinguish each phase by
observable quantities. The relationship of the present model with the
anisotropic rung-alternating ladder with spin-1/2 is also discussed.
