The word is cull. Culling of animals is done for many reasons, the main ones being to control populations and destroy pests. For example, irrigation in Australia has allowed kangaroo populations to explode but during times of drought, there is not enough grass to support them. To save them the pain of starving, many are shot. Rabbits and feral pigs, horses, goats and camels, which destroy the environment, are culled to preserve native species with baits, aerial shooting programs and traps.