Ok, so we know mogu are mortal; they were titan constructs and were afflicted by the Curse of Flesh (1). We also know they reproduce and have offspring/families (2). Mogu also have a finite lifespan, unlike draenei; Lei Shen is explicitly stated to have died of old age (3). So mogu are born, live, reproduce, and die, just like most other humanoids. No big deal, right? Except for one thing.
There are no women. Unlike kobolds, gnolls, ogres, etc, where we can just assume the females exist (either off-screen, or are physically identical to males unless you lift the loincloth), it's stated that there aren't any mogu women - "The Twin Consorts are said to be greatest of the Thunder King's treasures. Rumored to be the only known female mogu in existence, Lei Shen keeps his trophies close and their combined arsenal against interlopers closer." (4) Savvy readers will note the weasel words "rumored" and "known," but this is cliche fantasy land, where All Rumors Are True. So Lei Shen was a jealous pimp and killed all the other women and kept two for himself? A little weird, but I guess that works. Also, each time we kill this boss, we're condemning the mogu race to extinction for a few epics (isn't being a hero great?!)
Except that's not the case, because - "Players may have noticed the complete absence of any female mogu in their exploration of the continent of Pandaria. Players who look closely at the models of these celestial twins will note that they seem quite literally carved out of stone. Indeed, these were specifically created by Lei Shen and empowered to serve and guard him, and they are a direct reflection of his will rather than any broader sense of mogu culture as a whole." (5) So, the two female mogu aren't even real mogu, they're just constructs. Fun trivia for the raiders - the penultimate fight of Throne of Thunder is versus the Thunder King's sex toys.
So it's been at least 10,000 years since Lei Shen died (his palace was sunk by the Sundering (6)), and the mogu have been doing Elune-knows-what since then. But, presumably, their lifespan is less than that. And since there are no women, how have the mogu been breeding; hell, how did they do it before the Sundering? The only thing I can think of is that they're some sort of high-functioning planarian worm. Either they bud and create new mogu, or each mogu has, erm, both parts and one is chosen to carry the offspring. The second theory actually kinda fits their warlike and combative culture. Since each mogu has the potential to make more, there would be a lot of competition to have the honor of bearing children to carry on the legacy of a particular mogu.
So there ya go, folks, mogu are hermaphroditic. You may now sleep easy, knowing that this incredibly important question has been answered.
4. Dungeon Journal - Twin Consorts