The idea is that if you didn't amputate the limb, your death is certain. However, even if you did, your survival is not guaranteed
Feel free to write about any situation that you want to that you would/wouldn't do it in, but i have made two scenarios regardless:
1: The 127 hours scenario: Your limb is pinned by a unmovable object and you have no way to call for help. You are in a isolated area, and although people do occasionally visit it, No one will find you before you die of dehydration if you remain pinned by the rock. You must perform the amputation yourself, with your only tool being a penknife. If you did cut off the arm, Then you would have to find help before you did. apart from the knife, all you have are the clothes on your back
2: You have been bitten by a zombie. You have no painkillers, and your only tool is a bone saw. Your friend has volunteered to do the amputation for you. The bite is still fresh, so it could work.