The recent China earthquake has released dozens of landslides, which have blocked rivers. The water builds up behind them. What happens next, has happened to quite a few man-made earth dams, and it's not pretty.
The whole thing depends on the non-linearity of the erosion process. As the water over-tops an earthen dam, it starts to erode. Most man-made dams have concrete spillways, and asphalt or concrete on top. That way, water can be safely released.
But if the soil consists of loose sand or silt, then things are different. The water starts to form a gully, and more water starts to flow. Very quickly, it cuts through the whole dam, and a giant wall of water rolls down the valley.
With natural landslides, there may be a lot of boulders which slow down the process. Even digging a ditch, like the Chinese are doing, is playing with fire, since it could run away from them. As well, a release of an upper dam could start a chain reaction.