We introduce the concept of frequency-mixing intelligent reflecting surface (FMx-IRS), where the elements of the surface continuously change the phases of the incident signals. In this way, the FMx-IRS acts as a frequency mixer and makes the propagation environment nonlinear, thereby introducing new frequencies. We study the basic features of the proposed concept and demonstrate its advantages that stem from the novel type of control over the wireless propagation. The channel decoupling feature and the correlation between reflected channels are elaborated for the architecture, and are validated by the simulations.