I should have said they have anti-tamper devices, or some kind of proximity fuse. Some other posters mentioned the soviet PFM-1 mine, that's more what I'm taking about.
They'd lay in fields until something disturbs them, then they explode. Some livestock or wild animals would get blown up, but the intention would be to drop them among crops, and so the first thing to move them would be the farmer or a tractor. It's a different potential set of victims, with a different set of skills, and with different equipment being threatened. So now the government has to worry about replacing farmers and tractors, and placing air defences among a different part of their populace. A few raids of this type could distract attention from the cities enough to make a difference there. And even if they don't, if the intention is to demoralise the enemy civilian populace, this makes a whole other demographic feel like they are in the firing line.
Still a lot of issues.
1) I don't think the fuses/bombs you wanted existed back then. There are proximity fuses but they were basically small radars. Not the type of weapon to explode because someone walks 10 feet away.
2) It would not just be some livestock, but a lot of livestock/wild animals. For the mine fuse I know of that are designed to kill humans can be setoff with a few pounds of pressure. Small mammals (5KG and bigger) and many birds can easily generate this much force. Sure, blowing up a calf is a loss, but much less of a loss than a using the same tonnage in a city. Easily 10 animals for every human.
3) Randomly laying minefields work both ways. For the allies, if they heavily mine the lands behind the lines, they will then have to fight through these minefields. Open wheat fields also make good T-34 country.
4) No one will ever put air defense up to defend wheat fields.
5) Farmers are more adaptable and rugged than you appear to believe. Farming has a high accident rate compared to almost any other industry. They will adapt.
I agree it would do some damage, but it is not even the best way to destroy food. Bombing grain silos and small farming town will be more effective at destroying food or killing farm related humans than what you are proposing. On any given day, you might have a couple of farmers in a 40 acre field. There will be a few hundred to few thousand people in a 40 farming town and a grain storage facility will have 10's of workers. Area of effect weapons are used against high density targets before extremely low density targets. You are proposing huge amount of effort for extremely modest gains.