Strong-field ionization provides fundamental insight into light-matter interactions, encoding the structure of atoms and molecules on the sub-Ångström and sub-femtosecond scales. In this Letter, we explore an important new regime: strong-field ionization by two-color circularly polarized laser fields. In contrast to all past work using linearly polarized drivers, we probe electron trajectories that are driven in a 2D plane, thus separating the tunneling angle from the rescattering angle. This allows us to make several new findings. First, we observe a single-lobed electron distribution for co-rotating fields, and a three-lobed distribution for counter-rotating fields, providing the first experimental validation of the theoretical model explaining the generation of circularly polarized high harmonic light. Second, we discover that there is significant electron-ion rescattering using counter-rotating fields, but not with co-rotating fields. Finally, we show that the rescattered electrons are well separated from the directly-ionized electrons, in striking contrast to similar low-energy structures seen with linearly polarized fields. These findings help overcome the long-standing problem of how to decouple the tunneling and rescattering steps in strong-field ionization, which will enable new dynamic probes of atomic and molecular structure.