Nitrogen and Oxygen

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It essentially doesn't. It's the lack of Nitrogen that promotes Nitrogen off-gassing. However, you have to replace the Nitrogen with something.
 
There was once a belief among a very small segment of the diving community that it did do that. They called it the "oxygen window," a term that means something else by other people. The idea was that somehow very high PPO2s being converted to carbon dioxide create an "oxygen vacancy" that created more room for the nitrogen to leave. (That's the best I can explain it.)

If you think this violates both Dalton's Law and Henry's Law, that is what most people think, too.

I read the paper in which this was explained. As a non-scientist, I read carefully as it went through the observed data step by step. And then, in one magic paragraph, BAM! the idea was stated boldly, even though I could not see one iota of evidence for it in the data and discussion leading up to it. Other people were saying the same things. In Deco for Divers, Mark Powell dismissed it in a couple of sentences.

In accordance with that belief, one group of divers began to extend decompression stops when the PPO2 was at its highest, creating what they called an S-curve, in which deeper stops were longer than shallower stops. That group later decided that the theory was faulty and has dropped that practice. Another group that sprang out of that group still uses the S-curve, although I am not sure why, since I heard them admit years ago that the theory behind it was suspect.
 
It essentially doesn't. It's the lack of Nitrogen that promotes Nitrogen off-gassing. However, you have to replace the Nitrogen with something.
Yes, the key is the difference between the nitrogen percentage in the body and in the gas you are breathing. No nitrogen at all in the gas you are breathing gets rid of the most nitrogen each breath. You could breath 100% argon and get rid of nitrogen just as fast as breathing 100% oxygen. But you'd die.
 
In gases like nitrox, the high PPO2 is simply the cheapest way to get a lower PPN2.
 
In gases like nitrox, the high PPO2 is simply the cheapest way to get a lower PPN2.
That is, the cheapest *safe* way to get a lower PPN2. Hydrogen is even cheaper than oxygen, but has a couple of problems in its use.
 
How does oxygen promote evacuation of nitrogen? What is the mechanism?

There are lots of ways of looking at that question but I'll take a crack at it. I think Mark Powell's Deco for Divers does a pretty good job of explaining the concept of diffusion starting on page 30. I'm "guessing" that the intent of your question applies more to the transfer of diluent (Nitrogen and/or Helium) across the alveoli than in the blood stream itself. This quotation is from the top of Page 31:

The human lungs have a very high surface area relative to the size of the lungs (600 million alveoli with an area of 100m2) and the walls of the alveoli are very thin, just 1 cell thick, so the distance to be diffused is very short. The steep concentration gradient across the respiratory surface is maintained in two ways: by blood flow on one side which is constantly removing blood which has had a chance to exchange gas with the lungs and replacing it with blood from the body's tissues and by air flow on the other side which replaces the air in the lungs with air from the atmosphere...

Of course having less diluent (Nitrogen in Nitrox) limits the PPN2 which is the primary driving force behind the amount absorbed (ingassed) by tissues during the dive, which reduces the amount to remove (outgas) during decompression. Does this make sense and does it apply to the intent of your question?
 
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How does oxygen promote evacuation of nitrogen? What is the mechanism?
Practical Diffusion Concept of the Oxygen Window:
Enlarging the oxygen window can only occur when arterial PO2 is increased to a maximum tolerated value, either by increasing depth or increasing FiO2 of the gas mix, or both. Although enlarging the oxygen window may not directly affect tissue gas removal, it does directly affect tissue on-gassing during decompression, which affects the amount of time required to decompress the tissue. . . Breathing [100%] oxygen at a deeper depth has a theoretical advantage of a greater hydrostatic pressure to hold dissolved gas in solution [i.e. Limiting venous blood supersaturation and bubble formation] . . . [but] Oxygen toxicity clearly limits the oxygen window to much lower values [like at the maximal ppO2 convention of 1.6 ATA] during in-water diving operations.

Furthermore, inert gas [Nitrogen and/or Helium] elimination is independent of depth only during [100%] oxygen breathing. . . The gas partial pressure gradient for movement from tissue into blood is not controlled by ambient pressure; it is controlled by the gas partial pressure in the tissue and in arterial blood. As long as the arterial [inert] gas partial pressure is zero, the gradient for [inert] gas removal from tissue is maximal . . .It should be intrinsically obvious that removal of a gas from tissue can be speeded by elimination of the gas from the inspired mixture. If the arterial partial pressure of a gas is zero, then no gas will diffuse into tissue while the gas is diffusing out of the tissue. . .

Gas Exchange, Partial Pressure Gradients, and the Oxygen Window, Johnny E. Brian, Jr., M.D.

So to truly take advantage of the full efficiency of the "Oxygen Window", you would have to switch to 100% Oxygen at 18m/60ft (2.8 ATA) -->as in a Table 6 Treatment in a dry Hyperbaric Chamber. Obviously, this is not advisable for in-water decompression procedures (unless you're Brett Gilliam).
 
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Not a complete explanation, but an easy way to think about it is simple diffusion. Basically particles of high concentration, (ie N2 in the tissues and blood stream during deco), move to areas of low concentration (ie, freshly respirated blood when breathing O2).

"Diffusion

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.

Diffusion refers to the process of particles moving from an area of high concentration to one of low concentration. The rate of this movement is a function of temperature, viscosity of the medium, and the size (mass) of the particles. Diffusion results in the gradual mixing of materials, and eventually, it forms a homogeneous mixture."

I believe effusion also plays a role in off-gassing during decompression too.

Wikipedia actually uses respiration as an example to describe diffusion, bulk flow and Fick's Law. It's a good, light read: Diffusion - Wikipedia
 
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Diffusion occurs in one direction or the other depending on the concentration gradient. Molecules diffuse from higher concentration to lower concentration until they are equal. The higher the gradient, the quicker the diffusion. Thus, breathing a higher concentration of oxygen, 100% being the highest, increases the concentration gradient for nitrogen and facilitates diffusion outward, off-gassing.
 
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