What's the relationship between drag divergence Mach number and maximum operating limit Mach number? The drag divergence Mach number, also known as the force divergence Mach number, is the Mach number where drag waves start to form. The drag divergence Mach number is typically between 5 to 10 percents greater than the critical Mach number.

The maximum operating limit Mach number(Mmo) is the mach number beyond which aircraft start to suffer compressibility effects and flutters at high altitude. It's basically the high altitude version of Vne(Vmo).

My question is: what are the two Mach numbers' relationships? Is Mmo always higher than the drag divergence number? If so, how much? Or is it safe to assume that they are more or less the same?
They are unrelated definitions. Mmo is set by the designer with input from actual flight testing, Mmo is a maximum safe speed and is only concerned with practical operation and structural integrity. Mach divergence is a physics phenomena. Mmo can be much lower or higher than the Mach divergence from one aircraft to the next. Mmo has a similar purpose to Vne but Mmo is a more useful measure for high performance aircraft. 
It just happens that most commercial and large business jets are designed for high subsonic cruise so the design goal is to push divergence to higher speeds for more efficiency and Mmo ends up very close to Mach divergence.