Spectrum fragmentation has always been a major issue to overcome toward spectrally efficient Flex-Grid over Single-Mode Fiber dynamic optical networks and continues like so when evolving to Flex-Grid over Spatial Division Multiplexing (SDM). A possible strategy to eliminate its pernicious effects is to divide the available spectrum into several partitions, dedicating each one of them to only support connections with identical spectral requirements. In this way, a first-fit spectrum assignment ensures that spectral gaps at each spectral partition will always match the bandwidth needs of future connection requests. In this paper, we extend this strategy to be applicable to Flex-Grid/SDM dynamic optical networks. Furthermore, leveraging the spatial multiplicity offered by SDM, we also investigate spatial partitioning as an effective yet simpler and more easily manageable solution to also eliminate the spectrum fragmentation negative effects. Both strategies are numerically evaluated in two reference Flex-Grid/SDM backbone networks with × 7 spatial multiplicity, yielding noteworthy carried network load gains up to 18% versus a non-partitioned network scenario. When increasing the spatial multiplicities up to × 30, such gains tend to stabilize around 3–4%. Some results are also obtained under unexpected traffic profile deviations, showing that, even under moderate deviations, partitioning becomes beneficial. Comparing spectral and spatial partitioning, they tend to perform quite similar in all cases. This makes us advocate for spatial partitioning as a more interesting solution for spectrum fragmentation avoidance in this kind of networks.