Many times octopuses in senescence will become autophagous. That means that they will eat their arms. It is usually a sign that your octopus is very close to the end of it's life. Sometimes octopuses will develop this disease before senescence, and in that case it is a serious problem. However, I doubt that your octopus has the disease; he is most likely near the end of his life.
It doesn't sound like the disease, if he had that he would have bitten the arms off at the base, right where they join the body. This sounds like old age....unless you have something else in the tank which may be harassing your octopus?