Y chromosomes are thought to undergo progressive degeneration due to stepwise loss of recombination and subsequent reduction in selection efficiency. However, the timescales and evolutionary forces driving degeneration remain unclear. To investigate the evolution of sex chromosomes on multiple timescales, we generated a high-quality phased genome assembly of the massive older (<10MYA) and neo (<200,000 years) sex chromosomes in the XYY cytotype of the dioecious plant Rumex hastatulus and a hermaphroditic outgroup R. salicifolius. Our assemblies, supported by fluorescence in situ hybridization, confirmed that the neo-sex chromosomes were formed by two key events: an X-autosome fusion and a reciprocal translocation between the homologous autosome and the Y chromosome. The enormous sex-linked regions of the X (296 MB) and two Y chromosomes (503 MB) both evolved from large repeat-rich genomic regions with low recombination; however, the complete loss of recombination on the Y still led to over 30% gene loss and major rearrangements. In the older sex-linked region, there has been a significant increase in transposable element abundance, even into and near genes. In the neo sex-linked regions, we observed evidence of extensive rearrangements without gene degeneration and loss. Overall, we inferred significant degeneration during the first 10 million years of Y chromosome evolution but not on very short timescales. Our results indicate that even when sex chromosomes emerge from repetitive regions of already-low recombination, the complete loss of recombination on the Y chromosome still leads to a substantial increase in repetitive element content and gene degeneration.