We report transport measurements through a single-molecule magnet, the Mn12 derivative [Mn12O12(O2C-C6H4-SAc)16(H2O)4], in a single-molecule transistor geometry. Thiol groups connect the molecule to gold electrodes that are fabricated by electromigration. Striking observations are regions of complete current suppression and excitations of negative differential conductance on the energy scale of the anisotropy barrier of the molecule. Transport calculations, taking into account the high-spin ground state and magnetic excitations of the molecule, reveal a blocking mechanism of the current involving nondegenerate spin multiplets.