Some people say that reed cutters can save tons of money, some say that a broken reed is worthless.

Do they work well, and what are the disadvantages?

My band teacher has a reed cutter that I use. It is almost all advantage. They are easy to use, and can save almost any chip. THe only disadvantage is that the reed gets harder, and if you can`t play on a reed that hard it won`t work. But then what you do is put that reed in a safe place until you can play on it