Double ionization of neon with orthogonally polarized two-color (OTC) laser fields is investigated using coincidence momentum imaging. We show that the two-electron emission dynamics in nonsequential double ionization can be controlled by tuning the subcycle shape of the electric field of the OTC pulses. We demonstrate experimentally switching from correlated to anticorrelated two-electron emission, and control over the directionality of the two-electron emission. Simulations based on a semiclassical trajectory model qualitatively explain the experimental results by a subcycle dependence of the electron recollision time on the OTC field shape.