Because of their high photon flux, X-ray free-electron lasers (FEL) allow to resolve the structure of individual nanoparticles via coherent diffractive imaging (CDI) within a single X-ray pulse. Since the inevitable rapid destruction of the sample limits the achievable resolution, a thorough understanding of the spatiotemporal evolution of matter on the nanoscale following the irradiation is crucial. We present a technique to track X-ray induced structural changes in time and space by recording two consecutive diffraction patterns of the same single, free-flying nanoparticle, acquired separately on two large-area detectors opposite to each other, thus examining both the initial and evolved particle structure. We demonstrate the method at the extreme ultraviolet (XUV) and soft X-ray Free-electron LASer in Hamburg (FLASH), investigating xenon clusters as model systems. By splitting a single XUV pulse, two diffraction patterns from the same particle can be obtained. For focus intensities of about $2\cdot10^{12}\,\text{W/cm}^2$ we observe still largely intact clusters even at the longest delays of up to 650 picoseconds of the second pulse, indicating that in the highly absorbing systems the damage remains confined to one side of the cluster. Instead, in case of five times higher flux, the diffraction patterns show clear signatures of disintegration, namely increased diameters and density fluctuations in the fragmenting clusters. Future improvements to the accessible range of dynamics and time resolution of the approach are discussed.