Furs are peeled away from the head without the need to cut. The leather industry has also been known to use skins from animals which have died of natural causes. This source of skins tends to be inferior because if the animals have been lying around dead, the skins would have started to rot. Whilst any animal is alive, it's body and skin are protected from putrefaction and rotting. As soon as the animal is dead, putrefaction sets in.
Bacterial action starts immediately, causing a breakdown in the skin.
Therefore, something has to be done as soon as the animal has been flayed, to prevent the skin from beginning to putrify. In an ideal world, we would take the flayed skins from the animals and immediately start tanning them. This would need to be done within minutes of the animals having been flayed. But we don't live in such an ideal world, since the abattoirs and tanneries can be halfway around the world from each other. The process which is required to protect the skins is known as curing, and there are several ways in which this can be done.