Molecular magnets incorporate transition-metal ions with organic groups providing a bridge to mediate magnetic exchange interactions between the ions. Among them are star-shaped molecules in which antiferromagnetic couplings between the central and peripheral atoms are predominantly present. Those configurations lead to an appreciable spin moment in the nonfrustrated ground state. In spite of its topologically simple magnetic structure, the [(CrMn3II)-Mn-III(PyA)(6)Cl-3] (CrMn3) molecule, in which PyA represents the monoanion of syn-pyridine-2-aldoxime, exhibits nontrivial magnetic properties, which emerge from the combined action of single-ion anisotropy and frustration. In the present work, we elucidate the underlying electronic and magnetic properties of the heteronuclear, spin-frustrated CrMn3 molecule by applying X-ray magnetic circular dichroism (XMCD), as well as magnetization measurements in high magnetic fields, density functional theory, and ligand-field multiplet calculations. Quantum-model calculations based on a Heisenberg Hamiltonian augmented with local anisotropic terms enable us not only to improve the accuracy of the exchange interactions but also to determine the dominant local anisotropies. A discussion of the various spin Hamiltonian parameters not only leads to a validation of our element selective transition metal L edge XMCD spin moments at a magnetic field of 5 T and a temperature of 5 K but also allows us to monitor an interesting effect of anisotropy and frustration of the manganese and chromium ions.