Plaster casts can be removed by two means. They can be removed shortly before the next cast with a cast saw, which is vibrating bit/blade that usually can not hurt skin. If you put your finger on the blade, there will be no injury. In most cases should the cast saw cause an injury, it is minor. However, an experienced cast tech should not allow this to happen. If the padding under the cast is too thin however, this is a potential risk. These injuries are more of a skin "burn" than a cut, and will heal under the next cast. This is not always a reason to change doctors, but it may be a reason to ask for a different cast tech.
If your doctor cuts casts off you will be able to save your casts for posterity. Soaking casts off does not allow for this particular bit of memorabilia.
Soaking the casts off eliminates any risk of injury from the cast saw. Some parents and doctors prefer this method, while others are happy to get the cast removal done in a very short time. Soaking the cast off does take much longer, although it also allows you to bathe your baby at the same time. There is no "right" way to remove a cast, other than to make sure to do it within a couple hours of each next appointment for a new cast.
**There is study data that indicates that cast removal the night before increases cast frequency by half. The babies who had their casts removed the night before averaged 11 cast changes, vs the babies who removed the cast right before the appointment had on average 5 casts.
