The way that doctors or surgeons amputate is by cutting into the skin and then they tie off the blood vessels to prevent blood loss.
Then they cut and remove the blood vessels and other muscles that are needed to be cut and removed so that they can actually cut the leg or arm off.
Then they use an oscillating saw to actually cut the bone and then after the bone is cut the surgeon then uses excess skin that they left over to cover the bone after they cut it.
In the old days the surgeons used a wire saw that was operated by hand but the surgeons today use an electric saw that cuts through the bone easily.
Then they file down the bone before sealing your skin back up.
After an amputation you usually need to stay in the hospital for around 14 days so that they can monitor your health and make sure your health stays good after the amputation.