Does it mean that you are using X to save the world, or that you are saving the world by eliminating one X at a time?
Neither, and both.
Saving the world, one bug at a time - here the implication is that bugs will be destroyed one at a time until the world is saved.
Saving the world, one pixel at a time - this is a bit of a play on "save"; it's a photography blog, and the world is being "saved" on disk, one pixel at a time.
Save the world, one girl at a time - the salvation of the world will be the education of girls and women, which happens one girl at a time.
This is one of those memorable yet malleable catchphrases - "Zen and the art of X" is another - that stick in the viewer's mind, but can carry whatever message the user desires.
It is a mildly sarcastic (and often self-deprecating) statement. The person is not literally saving the world, but they are doing good. The individual gesture, the one X at a time, moves all of us one step closer to a good, safe, just condition.
The concept is similar to that suggested by Gandhi
Whatever you do will be insignificant, but it is very important that you do it.