Nonreciprocal devices, such as isolators, are required to protect sensitive superconducting quantum circuits. Growing research has focused on integrated alternatives to the existing bulky ferrite technologies. Here we realize a nonreciprocal isolator with a multimode microwave optomechanical circuit. Two mechanical oscillators mediate frequency conversion between two microwave modes. Relying on dissipation and the phases of the microwaves tones, the signals interfere constructively in one direction and destructively in the other, resulting in a nonreciprocal isolator. We show how this scheme can be extended to directional amplification and to a circulator, if an additional microwave mode is introduced.