Supposing the warhead yield was large enough to disrupt the vortex, it would only last for a few seconds. The funnel would likely resume again. You’re fighting against atmospheric currents... There’s a reason no one has developed anything to dissipate one yet.
You might only have seconds to try and stop a tornado, but you do usually have a few hours to stop the atmospheric conditions that create tornadoes.
It’s unfortunate nobody has figured out how to tap into the energy that is created when two differing atmospheric pressure areas collide and form these thunderstorm patterns.