I was driving by a neighbors and seen a circle of black buzzard( not Mexican?? maybe cousins) around a cow so I stopped to see if everything was ok and she had a new calf that was trying to get up she kept them at bay. I had one a couple years ago a brangus cow, they will fight off anything even me, her calf couldn't get up she was standing over it shading it and a circle of the same birds waiting I thought the calf was dead it's head was twisted back, the calf was fine after I got it from her and took them to the corral. I don't like them critters very well.
Here is what I've figured out after loosing still more cow/calf pairs.
The black buzzards wait around in the trees and circling waiting for the afterbirth. The caracara are the ones attacking the cow and calf during birthing. After that the black buzzards join in.
You couldn't shoot these things If you did get a permit, they fly too fast and low, skirting around a pasture at high speed like a Falcon.. They are vicious and have overpopulated with no natural predators.
In Texas it is legal to kill buzzards if they are destroying your livestock. You can get a permit from Texas Parks and Wildlife. Talk to you game warden or county ext agent, I got this information from our Game Warden in DeWitt County.
Got a .17 cal with a scope that works great.
I agree, Mexican eagles don't kill the calves, just waiting for something else to. But they do kill Gophers.
Buzzards will absolutely feed on living calves. Leg hold traps on tall posts might accidentally kill a buzzard if you bait it with dead rabbits. You have the right to protect your stock, and you should have the wisdom to do so quietly.
Here is how to build a trap for buzzards: with some 5 ft high hog wire that is small enough so the buzzards can't crawl thru, make a circle 5 ft or so in diameter held in place with posts, don't have to be big. Throw in something dead. The buzzards can not fly straight up, only at an angel. Therefore they can't get out and you got as pot shot. The only drawback is you have to clean the stinking dead ones out, A buzzard is smart enough not to eat something that smells that bad. They won't eat their own.