Can sound waves deform (curl brake) like water waves? As far as I understand, both water waves and sound waves are mechanical waves, in the sense that both are created by the relative movement of particles in a certain medium. Sound is propagation of waves in air (relative movement of air molecules), and water waves propagate in water (relative movement of water molecules).

You can see water waves to create something called a curl brake (when they tip over) as seen on the image. Since both sound waves and water waves are similar in that they both propagate on a medium, can sound waves deform, and for example create a curl brake (tip over) too?
Can sound waves deform (curl brake) like water waves?
 A: They cannot "curl" because the pressure cannot become multivalued. Because of non-linear effects they can, and do, steepen. But instead of breaking, they   form shockwaves in which there is very sharp jump in the pressure. An example of the steepening effect can be found in wikipedia under burgers equation
A: Water waves have both transverse components, where the oscillations are perpendicular to the direction of wave motion, and longitudinal components, where the oscillations are in the direction of wave motion.
In fact, water molecules follow a circular path (orbits) in water waves. When ocean waters reach shallower parts, the “orbitals” in the upper part of the wave are moving faster than those lower, and so the wave crest moves forward faster and ahead of the rest of the wave, creating the “tube” effect.
This is different to sound waves in air, in which case there exist only longitudinal oscillations in general.
So the "curl break" phenomena is not something that will occur for sound waves due to the fact that (in air) oscillations occur parallel to the direction of propagation.
You can imagine "curl break" to occur when a wave oscillates both up-and-down and in the direction of propagation like in water waves, but not for a wave that is purely longitudinal, as in sound waves (in air).
A: Perhaps the difference for unconfined waves in gases is that sound waves are spherical whereas those in seas are close to linear.
A: First, as correctly observed, waterwaves and soundwaves are both mechanical waves. The closest analogue to waterwaves are surface acoustic (sound) waves.
Sound waves in a solid may have both a transverse and a longitudinal component. For example, surface acoustic waves and Rayleigh waves have transverse components propagating on the surface of a solid.
However, breaking waves ("curl brake") occur only in surface waves in fluids, and not in a solid. This is because, when the shear strain is large enough, the solid would just break down into pieces, instead of realizing a breaking wave.
In a nutshell, surface mechanical waves in fluids can exhibit breaking waves ("curl brake"). Surface mechanical waves in solids, at certain regimes, may just break the solid into pieces instead.
Both breaking waves and broken solids are nonlinear effects, of course.
Sound waves in air may have shear transverse waves (even though they are kinda exotic). I don't see any physical reason why these shear waves could not break. However, I think breaking waves of these kind have never been observer. This looks like an open research question.
https://en.wikipedia.org/wiki/Surface_acoustic_wave
https://en.wikipedia.org/wiki/Rayleigh_wave
https://physicstoday.scitation.org/doi/10.1063/1.1472393
To cite the paper above:

The dramatic process of wave breaking cannot be observed in solids with SAWs, since solids usually break under strain as soon as a certain degree of bond extension (typically 10–20%) has been reached.

Edit:
Shear (transverse) waves may occur also in air.
https://physics.aps.org/articles/v10/57
Honestly, I think that whether shear waves in air may have breaking waves is an open question.
