Of the 18 currently present, if I absolutely had to cut one, Mongolia would be the one to go. They're a great civ, but so are all the others, and they edge out in one way or another.
1 - Historical Longevity
Mongolia did not last long as a notable civilization - 200 years if even that, before fading back into obscurity. That immediately make them less acceptable than a vast number of other civilizations. There are only four other comparably short-lived civilizations in C4 : America, the Aztecs, the Incans, and Mali.
2 - Historical Achievements :
All five of these nations conquered comparably large empire. Mongolia's was by far the largest, true, but they only conquered. America, whose empire comes closest in size to Mongolia, has countless other achievements to its name (first man on the moon, not to mention economic, cultural and political achievements), and that makes it a far superior choice to the Mongols. The other three, while smaller than Mongolia, also have other achievements to their name, whether architectural (Tenochtitlan), administrative (the Incan system), economic (Mali's trade empire), cultural (Timbuktu was a major center of learning), etc. They're about even with Mongolia, thus.
3 - Geographical Positioning.
The ability of a civ to fill a spot on the world map should be considered. Mongolia is useful, but not all THAT much - they fill a relatively un-habitable piece of land, on a continent (Asia) that does haev a few nations already. Bluntly put, Central and South America, and Sub-Saharan Africa, need civs in Mexico/Peru/the Sahel region a lot more than Asia need someone in the steppes to balance out the map.
Finally, the mongol's actual historical impact can be more-or-less filled in by the Barbs system in Civ IV (where they can actually take over cities). The same can't be said of the other three civs, so, bluntly put - Mongolia loses out.
That's only if I have to CUT one civ, though. If I have to trade civs, Aztecs go in favor of the Maya.