We study the low-temperature properties of a mixed ðS; sÞ ¼ ð3=2; 1=2Þ alternating quantum spin chain with antiferromagnetic-ferromagnetic bond alternation and single-ion anisotropy using spin-wave theory, density-matrix renormalization group calculations and exact diagonalization of finite clusters. An instance in this system is the recently synthesized bimetallic chain, which shows a novel magnetic behavior, namely, the x M T versus T curve decreases rapidly at low temperatures after displaying a pseudo-plateau around a certain intermediate temperature. There are two different mechanisms which could explain this unconventional feature: the zero-field splitting of the ground state and/or the ferromagnetic nature of the interdimer interactions. We clarify the role of these two kinds of mechanisms in the observed properties of the system by deviating from the otherwiseexpected ferrimagnetic ground state and considering a slight deviation from the decoupled-dimer limit, namely the description of the system by means of effective spin-1 ions at each unit cell with residual antiferromagnetic interactions, which is consistent with the antiferromagnetic-ferromagnetic bond alternation.