Which galaxy is receding from the Milky Way the fastest? What is known of the mechanism behind its recession? Galaxies are always in motion relative to the Milky Way. My question is, which galaxy is receding the fastest from our viewpoint?

What is the theorised mechanism that causes this?
This question may be a duplicate to: On what scale does the universe expand?

The mechanism for the expansion of the universe is gravity, manifested through what's known as Dark Energy. Dark Energy is a component to the universe which today, composes 68.3% of the energy density of the universe. You may be confused as to how gravity could be responsible for the expansion of the universe, but the equation of state of DE, 

w = pressure/density


is negative (w_DE = -1), which means that it has anti-gravitational properties. Additionally, its density remains constant as the coordinates of the universe change, which is the reason why it dominates later on in the universe's history (while all other components, matter (dark or otherwise) and radiation/relativistic matter, become diluted with the expansion of the universe).

To answer your question, because the expansion of the universe is happening at all points in space, it looks like the "center" of expansion is at every point in space (see: Space expansion in layman terms), the galaxies furthest away (highest redshift), are the ones moving quickest away from the Milky Way Galaxy.