Many poems suggest particular emotions and William Stafford's poem "Traveling Through the Dark" is no different. Interpreting the mood of a poem is difficult though given different readers may come up with different emotions felt when reading any given poem (or text).
Based upon Reader-Response, the specific emotions suggested in Stafford's poem are both sorrow and compassion.
The following lines suggest the sorrow the speaker feels as the car lights illuminate the swollen and pregnant belly of the dead doe.
My fingers touching her side brought me the reason--
her side was warm; her fawn lay there waiting,
alive, still, never to be born.
The speaker has compassion for the doe, and other deer, which may walk into the path of an oncoming car (or the speaker's car if forced to swerve) and "might make more dead." The speaker not only worries that swerving will cause another death, he (assumptive given the poet's gender) knows that the baby deer, still alive, has no chance at life. The speaker has no other choice than to push her "over the edge into the river."
Therefore, the compassion that the speaker feels can be picked up by a reader. An engaged reader can relate to the compassion the speaker feels and, most likely, would "swerve" when making the decision to end the baby deer's life to save it from suffering.
Overall, the first section engages the reader and forces them to feel sorrow for the dead deer. Once the reader finds out about the living baby deer, the sorrow changes and becomes compassion. In the end, some may find that the actions of the speaker are wrong--his compassion should have made him wish to save the deer. Instead, it is his compassion which pushes him to save the baby deer any more pain in life.