Is a livestock breeder sinful if he holds a small goat so that a large male goat can mount her, which leads to her becoming pregnant with twins that she is unable to deliver, resulting in her death?

The Sharia (definition) prohibits killing or torturing animals without cause. The proof for this is the noble Hadith (definition): "A woman entered the Hellfire because of a cat that she tied up. She neither fed it nor gave it water, nor did she leave it to eat from the vermin of the earth." As for what the breeder did, there is no prohibition against it, and the default rule for actions is permissibility unless there is a specific prohibition.