The irony of loyalty
Hondo is first depicted in his relationship to the U.S. Army leads the reader to be surprised when Hondo reveals what amounts to dual citizenship. Ironically, Hondo has been able to both fight against the Apaches, and also to live amongst them, using specific loyalties to specific people, instead of fighting for principles or ideas. In a sense, he has abandoned portions of his personality in order to be more able to live at peace in a world of bitter conflict.
The irony of mercy
This is another central paradox at the heart of the story, that Hondo's mercy is not necessarily in the form of sparing someone's life. Sometimes, mercy means killing someone quickly instead of dragging it out in torture. He kills Ed Lowe and Silva and takes no pride in it. In a way, his willingness to kill is part of what mercy means for Hondo.
The irony of brutality
In the context of the deep communal loyalty that exists among the Apaches, the reader sees a double-sided personality among the Natives. On one side, there is the brutality, the willingness to kill, and even to torture, but on the other side, the reader sees the thoughtful, fair leadership of Vittoro, along with his eagerness to reward virtuous attitudes. The effect of such violent fairness is that their society is beautiful and peaceful. So ironically, brutality and peace do coexist for the Apaches.
The irony of the desert
This narrative does something with setting and context by showing off the beauty of the desert, as well as the beauty of the survivalist lifeforms that exist in the desert. The desert could be seen as a lifeless void, especially by those who have never seen one in person. But in this story, the desert is the perfect setting for this story, because the vitality of the desert is a fierce devotion to life, in spite of the brutal reality of the situation.
The irony of humanism
By refusing to give into easy narrative shortcuts, the characters emerge from the plot, each of them governed by different principles and motives. In other words, just like Hondo himself, the story is dual in nature. It doesn't show one group as better or worse than another. The only evil seen in the narrative comes when someone is willing to cheat or manipulate. This humanist perspective is ironic when one considers that this is a story about warfare.