The problem is that when you are inside the submarine you usually get more or less normal atmospheric pressure (maybe a little higher). What keeps the submarine from imploding is the structural resistance of the hull (usually an inner and an outer hull).
The water pressure at the Challenger deep is in the order of 1100 bar (8 tons per square inch). So if you opened the lid, the volume of the air would be compressed to about 1/1100 of its original volume. Assuming an air volume of 3 m^3, all that would be compressed to roughly 3 liters of air.
But the biggest problem would be that while 70% of our body is water (and incompressible), our lungs and internal cavities are filled with air. So what would happen is that the air inside of our torso would be collapsed to almost 1/1000 of its original volume. Additionally, it would probably be very difficult to breathe (ie. flex our muscles to fill our lungs with air) due to the external load.
fluid pressure on boundaries
The following is from a lecture on fluid mechanics. It shows the fluid pressure direction on different boundaries.
What should be evident, is that pressure is always normal to the surface boundary. I.e. pressure can act in all directions. So, what happens when a can is submerged in water is the following
You might notice that the pressure above is less than the pressure below (so for a thin object the pressure difference would not be significant). This is how buoyancy force is generated. However, this is not the discussion here, and you can just consider that the pressure is all around equal.
On the other hand, the air inside the submarine is exerting pressure on the walls - again normal to the walls. Its more or less like a balloon in the figure below
So what would happen if you opened the bottom hatch in the submersible y, what happens is that now you have a water air boundary. On one side there is a 1atm air and in the other its about 1000atm pushing the other way.