Spatial light modulators (SLMs) are the most relevant technology for dynamic wavefront manipulation. They find diverse applications ranging from novel displays to optical and quantum communications. Among commercial SLMs for phase modulation, Liquid Crystal on Silicon (LCoS) offers the smallest pixel size and, thus, the most precise phase mapping and largest field of view (FOV). Further pixel miniaturization, however, is not possible in these devices due to inter-pixel cross-talks, which follow from the high driving voltages needed to modulate the thick liquid crystal (LC) cells that are necessary for full phase control. Newly introduced metasurface-based SLMs provide means for pixel miniaturization by modulating the phase via resonance tuning. These devices, however, are intrinsically monochromatic, limiting their use in applications requiring multi-wavelength operation. Here, we introduce a novel design allowing small pixel and multi-spectral operation. Based on LC-tunable Fabry-Perot nanocavities engineered to support multiple resonances across the visible range (including red, green and blue wavelengths), our design provides continuous 2π phase modulation with high reflectance at each of the operating wavelengths. Experimentally, we realize a device with 96 pixels (~1 μm pitch) that can be individually addressed by electrical biases. Using it, we first demonstrate multi-spectral programmable beam steering with FOV~18° and absolute efficiencies exceeding 40%. Then, we reprogram the device to achieve multi-spectral lensing with tunable focal distance and efficiencies ~27%. Our design paves the way towards a new class of SLM for future applications in displays, optical computing and beyond.