Whether or not we could ever engineer such a thing is uncertain.
Usama Kadri, a mathematician at Cardiff University in the UK, has published new calculations in the open-access journal Heliyon demonstrating the possibility of neutralizing tsunamis with underwater sound waves. While actually implementing such a scheme would be enormously expensive and an enormous technical challenge, there aren't a whole lot of other tsunami defenses that don't basically just reduce to "getting the fuck to high ground before the wave hits." So, it's pretty novel.
The sound waves in question are more properly known as acoustic gravity waves (AGWs): vast underwater waves that travel at the speed of sound and are generated naturally by earthquakes and other geological events. In a sense, Kadri is then proposing fighting fire with fire. AGWs form naturally with tsunamis and act as subsurface precursors to the main event, affecting disturbances to the water column all the way from the surface to the seabed. AGW detection has recently been proposed as a an early-warning mechanism for tsunamis and rogue waves.
"Besides acting as tsunami precursors, AGWs can exchange and share energy with surface ocean waves," Kadri explains. This exchange occurs in an interaction known as the resonant triad, which is probably easier to just visualize.
The catch with the above setup, where a single smaller wave (an AGW) is used to drain energy from a much larger wave, is that it results in the creation of a second AGW and the two AGWs just wind up swapping energy amongst themselves rather than draining off energy from the tsunami. Kadri's answer to this is to start with two AGWs. The two AGWs moving at a much faster speed and in the opposite direction of the tsunami quickly sap away energy from the larger wave and scoot it far away.
The tsunami doesn't just die, but the interaction leaves it significantly weaker. And "significantly weaker" could mean saving hundreds of thousands of lives and billions of dollars in property damage, as in the case of the 2004 Indian Ocean earthquake and tsunami (Kadri's example). Unfortunately, this is all easier calculated than done.
"The amount of energy required to generate AGWs, given a realistic scenario, is probably much higher than the AGW energy, whereas the associated amplitude reduction is probably far less efficient," Kadri concedes. "Thus, there is a need to improve the interaction efficiency further."
But there's a deeper problem. The wavelengths of the AGWs required to have an effect on the tsunami are so long that it's difficult to imagine them being produced mechanistically at all. Kadri imagines that it may be possible to harness the same AGWs produced by the earthquake that produced the tsunami to somehow reflect back at the tsunami in modulated form. That's a pretty vague possibility.
"While detection is relatively straight forward," Kadri concludes, "the mitigation of tsunamis requires the design of highly accurate AGW frequency transmitters or modulators, which is a rather challenging and ongoing engineering problem.