When the girl speaks 'supper', the saw comes at his hand. When he is at the doctor, the boy doesn't realize the hand is gone and asks his sister not to let the doctor cut it off. Then, the doctor was watching him, then began to listen to his heartbeat or his pulse, when he realized there was "Little-- Less-- Nothing!!" they realized the boy was dead. Further research on the true story of the poem suggests that he died off going into shock and then heart failure.
Sources: https://allpoetry.com/Out,-Out--
