In populations with mixed vaccination status, testing programs focused on only the unvaccinated population are being enacted to mitigate SARS-CoV-2 spread. However, it is not well understood how viral spread occurs in mixed-status populations, including the possible benefits of unvaccinated-only testing. Here, we analyze a model of SARS-CoV-2 transmission in which a variable fraction of the population is fully vaccinated and unvaccinated individuals are proactively tested for infection, while varying transmission rates, vaccine effectiveness (VE) parameters, and prior infection rates. This analysis reveals principles of viral spread in communities of mixed vaccination status, with implications for testing policies. As vaccination rates increase, the proportions of infections occurring in unvaccinated individuals and the amount of transmission driven by the unvaccinated both decrease, such that at ∼65-75% vaccine coverage, most infections are vaccine breakthroughs, and at ∼76-83% vaccine coverage, most community spread is driven by breakthrough infections, under baseline mRNA VE assumptions. These ranges shift lower with waning VE and higher with boosted VE. In highly vaccinated communities proactive unvaccinated-only testing had little impact on community spread. Instead, the benefits of weekly unvaccinated-only testing were restricted to regimes with high or moderate ongoing transmission due to lower vaccination rates and strongly depended on near-perfect test compliance. By evaluating a wide range of scenarios, this work finds broadly that resources devoted to routine unvaccinated-only testing could be reallocated when vaccine coverage is sufficiently high.