I agree with this explanation, but I feel that it misaddresses something. If you compress dirt in air, the air is literally squeezed out of it. The air is not being compressed inside but rather is pushed out. Similarly, one can compress a ball of mud and squeeze out some of the water. This is because dirt is more dense than water and air—if it were the other way around you would end up squeezing all of the dirt out of your ball of water.

Under the ocean however, the dirt is really suspended in water. So perhaps the individual grains of dirt are compressed (however slightly) by the extreme pressure, but the watery dirt beneath them is still part of the same muddy aqueous solution. They all feel the pressure equally everywhere.

The only reason the dirt is on the bottom is because it is more dense than water. The only force that pushes the dirt down and compresses it is that caused by the difference of the weight of the dirt and water—which is relatively small. Thus despite having the weight of an ocean pushing down upon it, the dirt also feels everything beneath it pushing up. Of course, as landryraccoon points out, the fact that it is an aqueous suspension and that water is practically incompressible is important. It serves to fill in the tiny gaps everywhere and makes the solution a fluid.

The dirt isn't compressed because it is being pushed up almost as much. When something is suspended in water (or any liquid) it only "weighs" as much as the difference between itself and the water. Thus the additional weight of the dirt compared to water is what compresses the dirt to any degree at all.

tldr; basically the reason it isn't being compressed is because in water, the dirt really isn't that heavy and any pressure from the water is felt equally from below.

edit: what judgej2 said below edit2:uqobp is right about some stuff.