Computer-generated holography (CGH) is a promising technology for next-generation displays. However, generating high-speed, high-quality holographic video requires both high frame rate display and efficient computation, but is constrained by two key limitations: ($i$) Learning-based models often produce over-smoothed phases with narrow angular spectra, causing severe color crosstalk in high frame rate full-color displays such as depth-division multiplexing and thus resulting in a trade-off between frame rate and color fidelity. ($ii$) Existing frame-by-frame optimization methods typically optimize frames independently, neglecting spatial-temporal correlations between consecutive frames and leading to computationally inefficient solutions. To overcome these challenges, in this paper, we propose a novel high-speed full-color video CGH generation scheme. First, we introduce Spectrum-Guided Depth Division Multiplexing (SGDDM), which optimizes phase distributions via frequency modulation, enabling high-fidelity full-color display at high frame rates. Second, we present HoloMamba, a lightweight asymmetric Mamba-Unet architecture that explicitly models spatial-temporal correlations across video sequences to enhance reconstruction quality and computational efficiency. Extensive simulated and real-world experiments demonstrate that SGDDM achieves high-fidelity full-color display without compromise in frame rate, while HoloMamba generates FHD (1080p) full-color holographic video at over 260 FPS, more than 2.6$\times$ faster than the prior state-of-the-art Divide-Conquer-and-Merge Strategy.