A defective cubane-shaped heterometallic trinuclear (Co2DyIII)-Dy-III compound with only one magnetically interesting ion (Dy-III) has been assembled by virtue of a multifunctional acylhydrazone ligand. Because of the nonaxial ground state of Dy-III ion derived from a low-symmetrical crystal field, the title compound displays field-induced multiple relaxation processes which are of molecular and a dipolardipolar coupling origin, as revealed by combined experimental and theoretical investigations. The results demonstrate that such a mononuclear dysprosium(III) compound with a low-symmetrical environment of magnetic center appears to be a model system for further investigations to shed light on the complex relaxation mechanism of lanthanide-based single ion magnets.