How are animals processed for organic meat killed?
Same way the rest of them are. Organic refers ONLY to how the animals are fed and whether or not chemicals (hormones, steroids and antibiotics) are used in their rearing. It says nothing about how the animals are treated, their quality of life, or the cruelty of their death. Organic meat may arguably be healthier to consume, but if your concern is animal cruelty, organic meat is meaningless.