  The mixed spin-(1/2, S_B, S_C) Ising model on a decorated square lattice with
two different kinds of decorating spins S_B and S_C placed on its horizontal
and vertical bonds, respectively, is exactly solved by establishing a precise
mapping relationship with the corresponding spin-1/2 Ising model on an
anisotropic square (rectangular) lattice. The effect of uniaxial single-ion
anisotropy acting on both types of decorating spins S_B and S_C is examined in
particular. If decorating spins S_B and S_C are integer and half-odd-integer,
respectively, or if the reverse is the case, the model under investigation
displays a very peculiar critical behavior beared on the spontaneously ordered
'quasi-1D' spin system, which appears as a result of the single-ion anisotropy
strengthening. We have found convincing evidence that this remarkable
spontaneous ordering virtually arises even though all integer-valued decorating
spins tend towards their 'non-magnetic' spin state S=0 and the system becomes
disordered only upon further increase of the single-ion anisotropy. The
single-ion anisotropy parameter is also at an origin of various temperature
dependences of the total magnetization when imposing the pure ferrimagnetic or
the mixed ferro-ferrimagnetic character of the spin arrangement.
