This is a folk song, whether written originally for a theater play or "borrowed" for it from a more ancient tradition. It is in the genre of a folk song.
Many folk songs are protest songs. They supposedly tell a tale, a mere story, but there is a message in them.
In "Dona Dona", the message is within the context of Jewish culture. This is a culture of humor and irony, for various reasons... Because its people are well educated and knowledgeable in their literary tradition, which makes allusions and and subtlety possible. Also, because the life of hardship and persecution in foreign lands made subtle, ironic communication necessary, and humor - essential.
My interpretation of the song: The song shows the cruelty and callousness of the farmer - the farmer is the slayer of the calf, note this! But he blames the calf. Of course the calf can't help being a calf, but this is exactly what the song is out to show. And in the background is the wind, or fate, or maybe even God - laughing in the field. The calf, destined to be slaughtered, supposedly sees the swallow and envies it, and hears the rustling of the corn in the field, and it sounds like the wind laughing... As if Fate, or God, or the wind, laughs instead of intervening on his behalf.
The song portrays the cruel fate of all who are bound and destined for slaughter. It is symbolic of the Holocaust and of the persecution of the Jewish people, but can apply to all persecuted people.
In noting the irony of the song, we can think of a famous Jewish proverb: "Man tracht, Got lacht". Man plans, God laughs - we are small and helpless in the face of Fate, or God, who turns our plans upside down for amusement. Fate, or God, has the last word - or laugh - and the same happens in Dona Dona. The poor calf is lead to slaughter, and the wind only laughs in response...
Isn't this what happened in reality?