You can't surf a tsunami because it doesn’t have a face. Many people have the misconception that a tsunami wave will resemble the 25-foot waves at Jaws, Waimea or Maverick's, but this is incorrect: those waves look nothing like a tsunami. On the contrary, a tsunami wave approaching land is more like a wall of whitewater. It doesn’t stack up cleanly into a breaking wave; only a portion of the wave is able to stack up tall. Since the wave is 100 miles long and the tail end of the wave is still traveling at 500 mph, the shore end of the wave becomes extremely thick, and is forced to run far inland, over streets and trees and houses.
If you're a surfer, you know how little control you have if your board is in whitewater. On a tsunami, there's no face, so there's nothing for a surfboard to grip. And remember, the water isn't clean, but filled with everything dredged up from the sea floor and the land the wave runs over--garbage, parking meters, pieces of buildings, dead animals. This is not what you want to be caught paddling around in. You can't duck-dive because the entire water column is in motion, not just the top few feet. You can't exit the wave, either, because the trough behind is 100 miles away, and all that water is moving towards you.
Big-wave riders should save their talents--and their lives--for big waves that are generated by massive storms. The only safe place to be during a tsunami is far inland and up on high ground.