Soil being washed away by the flow of water?

When soil is washed away by a flow of water, this is called erosion.

Erosion means the process of being gradually worn away, or the transport of minerals and materials naturally by wind or water.

The flow of water itself is called runoff.

Runoff is any water on the surface of Earth that is in motion. This includes anything from rivers to even a couple droplets of water flowing down a hill or something.

So the answer to your question is erosion is what washes away the soil by water.

Erosion is the name for soil being eroded upon by water wind or other natural things.