Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity.