Metasurfaces are ultrathin structures which are constituted by an array of subwavelength scatterers with designable scattering responses. They have opened up unprecedented exciting opportunities for extraordinary wave engineering processes. On the other hand, frequency converters have drawn wide attention due to their vital applications in telecommunication systems, health care devices, radio astronomy, military radars and biological sensing systems. Here, we show that a spurious-free and linear frequency converter metasurface can be realized by leveraging unique properties of engineered transmissive temporal supercells. Such a metasurface is formed by time-modulated supercells; themselves are composed of temporal and static patch resonators and phase shifters. This represents the first frequency converter metasurface possessing large frequency conversion ratio with controllable frequency bands and transmission magnitude. In contrast to conventional nonlinear mixers, the proposed temporal frequency converter offers a linear response. In addition, by taking advantage of the proposed surface-interconnector-phaser-surface (SIPS) architecture, a spurious-free and linear frequency conversion is achievable, where all undesired mixing products are strongly suppressed. The proposed metasurface may be digitally controlled and programmed through a field programmable gate array. This makes the spurious-free and linear frequency converter metasurface a prominent solution for wireless and satellite telecommunication systems, as well as invisibility cloaks and radars. This study opens a way to realize more complicated and enhanced-efficiency spectrum-changing metasurface.