Most people have, at some point, met a pet with only three legs. The reasons for amputating animals' limbs are as wide and varied as the reasons in humans.
Some pets develop tumours such as osteosarcomas, which sit in the bone and spread round the body. These can be painful and even when the tumour might have already spread, amputation may be the safest way to ensure future comfort. Other pets break their limbs and while most fractures can now be repaired, sometimes this is incredibly fiddly with a high risk of failure.