As I understand it, when the Mongols finally got inside of Baghdad they killed everyone and sacked the city.
Genghis Khan and the Making of the Modern World by Jack Weatherford has some insights on this topic.
The gist is that the Mongols only conducted massive destruction-and-slaughter operations once in a while: This was meant to communicate that anyone that tried to resist conquest would pay for it dearly. They gave this treatment to a number of large cities, such as Samarkand and Herat, besides Baghdad.
To just surrender was far better: The Mongolians didn't demand too much from their subjects (low taxes, for example), so one could consider their approach to be carrot-and-stick beyond straight fear tactics.
As for moral justifications... anything I have would be speculation.
Also see: [Genghis Khan: Life, Death, and Resurrection By John Man] (http://books.google.com/books?id=OXTv9a0HZakC&printsec=frontcover&vq=death#v=onepage&q&f=false)