Ocean tracers such as carbon dioxide, nutrients, plankton, and oil advect, diffuse, and react primarily in the oceanic mixed layer where air-sea gas exchange occurs and light is plentiful for photosynthesis. There can be substantial heterogeneity in the spatial distributions of these tracers due to turbulent stirring, particularly in the submesoscale range where partly geostrophic fronts and eddies and small-scale three-dimensional turbulence are simultaneously active. In this study, a large eddy simulation spanning horizontal scales from 20 km down to 5 m is used to examine the effects of multiscale turbulent mixing on nonreactive passive ocean tracers from interior and sea-surface sources. The simulation includes the effects of both wave-driven Langmuir turbulence and submesoscale eddies, and tracers with different initial and boundary conditions are examined in order to understand the respective impacts of small-scale and submesoscale motions on tracer transport. Tracer properties are characterized using spatial fields and statistics, multiscale fluxes, and spectra, and the results detail how tracer mixing depends on air-sea tracer flux rate, tracer release depth, and flow regime. Although vertical fluxes of buoyancy by submesoscale eddies compete with mixing by Langmuir turbulence, vertical fluxes of tracers are often dominated by Langmuir turbulence, particularly for tracers that are released near the mixed-layer base or that dissolve rapidly through the surface, even in regions with pronounced submesoscale activity. Early in the evolution of some tracers, negative eddy diffusivities occur co-located with regions of negative potential vorticity, suggesting that symmetric instabilities or other submesoscale phenomenon may act to oppose turbulent mixing.