We present optical, H I, and radio continuum observations of the highly inclined Virgo Cluster Sc galaxy NGC 4402, which show evidence for ram pressure stripping and dense cloud ablation. Very Large Array H I and radio continuum maps show a truncated gas disk and emission to the northwest of the main disk emission. In particular, the radio continuum emission is asymmetrically extended to the north and skewed to the west. The Hα image shows numerous H II complexes along the southern edge of the gas disk, possibly indicating star formation triggered by the intracluster medium (ICM) pressure. Our BVR images at 05 resolution obtained with the WIYN Tip-Tilt Imager show a remarkable dust lane morphology: at half the optical radius, the dust lane of the galaxy curves up and out of the disk, matching the H I morphology. Large dust plumes extend upward for ~1.5 kpc from luminous young star clusters at the southeast edge of the truncated gas disk. These star clusters are very blue, indicating very little dust reddening, which suggests dust blown away by an ICM wind at the leading edge of the interaction. To the south of the main ridge of interstellar material, where the galaxy is relatively clean of gas and dust, we have discovered 1 kpc long linear dust filaments with a position angle that matches the extraplanar radio continuum tail; we interpret this angle as the projected ICM wind direction. One of the observed dust filaments has an H II region at its head. We interpret these dust filaments as large, dense clouds that were initially left behind as the low-density interstellar medium was stripped but were then ablated by the ICM wind. These results provide striking new evidence on the fate of molecular clouds in stripped cluster galaxies.