We present an X-ray imaging and spectroscopic study of a partially occulted (N16W93) C7.7 flare on 2003 April 24 observed by Reuven Ramaty High Energy Solar Spectroscopy Imager that accompanied a prominence eruption observed by Transition Region and Coronal Explorer. (1) The activation and rise of the prominence occurs during the preheating phase of the flare. The initial X-ray emission appears as a single coronal source at one leg of the prominence and it then splits into a double source. Such a source splitting happens three times, each coinciding with an increased X-ray flux and plasma temperature, suggestive of fast reconnection in a localized current sheet and an enhanced energy-release rate. In the late stage of this phase, the prominence displays a helical structure. These observations are consistent with the tether-cutting and/or kink-instability model for triggering solar eruptions. (2) The eruption of the prominence takes place during the flare impulsive phase. Since then, there appear signatures predicted by the classical model of two-ribbon flares occurring in a vertical current sheet trailing an eruption. These signatures include an extreme-ultraviolet (EUV) cusp and current-sheet-like feature (or ridge) above it. There is also X-ray emission along the EUV ridge both below and above the cusp, which in both regions appears closer to the cusp at higher energies in the thermal regime (20 keV). This trend is reversed in the nonthermal regime. (3) Spectral analysis indicates thermal X-rays from all sources throughout the flare, while during the impulsive phase there is additional nonthermal emission which primarily comes from the coronal source below the cusp. This source also has a lower temperature (T = 20 ± 1 vs. 25 ± 1 MK), a higher emission measure (EM = (3.3 ± 0.4) vs. (1.2 ± 0.4) × 10⁴⁷ cm^–3), and a harder nonthermal spectrum (electron power-law index δ = 5.4 ± 0.4 vs. 8 ± 1) than the upper sources.