A frequency mixer is a nonlinear device that combines electromagnetic waves to create waves at new frequencies. Mixers are ubiquitous components in modern radio-frequency technology and microwave signal processing. The development of versatile frequency mixers for optical frequencies remains challenging: such devices generally rely on weak nonlinear optical processes and, thus, must satisfy phase-matching conditions. Here we utilize a GaAs-based dielectric metasurface to demonstrate an optical frequency mixer that concurrently generates eleven new frequencies spanning the ultraviolet to near-infrared. The even and odd order nonlinearities of GaAs enable our observation of second-harmonic, third-harmonic, and fourth-harmonic generation, sum-frequency generation, two-photon absorption-induced photoluminescence, four-wave mixing and six-wave mixing. The simultaneous occurrence of these seven nonlinear processes is assisted by the combined effects of strong intrinsic material nonlinearities, enhanced electromagnetic fields, and relaxed phase-matching requirements. Such ultracompact optical mixers may enable a plethora of applications in biology, chemistry, sensing, communications, and quantum optics.