It is usually best to roll them into the canyon: that road is narrow; to swerve might make more dead. (3-4)
The speaker knows what to do with the dead. He knows how precarious the road of life is, how easy it is to run off the road. And he knows that deviating (swerving) from the proper life path might have negative consequences. It sounds like this guy has been on "that road" for a while and knows what to do.
My fingers touching her side brought me the reason— her side was warm; her fawn lay there waiting, alive, still, never to be born. (9-11)
If you were in the speaker's position, would you be able to tell that the doe was pregnant by touching her side? These lines give us important information about the speaker. Not only do they let us know that the speaker is knowledgeable in the ways of the natural world, they also tell us he is a very perceptive person. He takes the time to notice things. He is aware: aware of how the dead doe's body feels on his fingers, aware of the fate that awaits the fawn, and aware of the part that he must play in the fawn's death.
I thought hard for us all—my only swerving— then pushed her over the edge into the river. (17-18)
Our speaker isn't the kind of guy that goes around blindly pushing pregnant deer off cliffs. He's a thinker. In fact, he "thought hard for us all." We can read "us all" as humanity. But it could also refer to the little group on the edge of the road: the speaker, the doe, and her fawn. Even though the speaker knows what he must do, he pauses to consider the impact of his actions on the three. He knows that he is the one that will bare the pain of the event far down the road. He is wise enough to know that an action can be difficult and painful and still be right.