While Erik and Bowlturner have given good answers, I will suggest that evolution would discourage such abilities.
As the starfish creature ascends to sentience, more and more brainpower is being used to manipulate symbols and concepts, and presumably manipulating appendages at the ends of each arm. A complex visual processing system is also being developed (at the simplest, I would think one eye per segment, but there might be hundreds of tiny eyes scattered across the creature). In an aquatic environment, the senses of taste and smell would also be vitally important, so a good chunk of brain is working on that as well. In addition, the creature might have other senses, for example, the ability to register electrical fields (much like sharks have to sense the presence of potential prey).
When the creature was still a primitive starfish, the sense organs would have become highly developed and lots of brain power devoted to that. Regenerating after being ripped in half made it important that the surviving part(s) could still sense possible predators while regenerating, so the Starfish ability to renew makes sense.
As the creature gets more advanced, the "frontal lobes" (or whatever the equivalent in this being) need to become more and more powerful, and take more and more of the processing power and life support. Being severed by a predatory beast or enemy starfish wielding an obsidian axe is going to be massively disruptive to the higher part of the brain, and while the human and mammalian brains are very plastic, I suspect the limits are not high enough for a full fledged separation.
The regrowing of a lot of higher order brain tissue is not going to be enough, since the surviving half(s) of the creature will also need to learn everything all over again to replace the knowledge and memories lost in the destroyed parts of the brain. The evolutionary disadvantage of devoting so much metabolic process to being prepared to regenerate is probably going to highly disadvantage the beings who retain this compared to the ones who have "streamlined" their metabolisms and nervous systems. They will be simply out-thought by any non regenerating sub species.
Of course, in the very long run, as they become technologically more advanced, they may eventually discover ways to re engage these metabolic pathways via surgery or advanced genetic engineering or stem cells, much like human scientists are working of discovering how we could regenerate limbs.