If psychopathic murderers truly lack the capacity to control their behavior, they should not be eligible for the death penalty.
Our entire legal system is rooted in the idea that people can only be liable for actions that they are able to understand and in some way control. We do not hold children as responsible for their actions as adults since we do not believe that they are old enough to understand and control those actions. We distinguish between murders that were committed with and without premeditation. These things show that we care greatly about the level of responsibility on the part of the criminal.
If psychopaths truly cannot control their actions, then they are not morally liable for those actions. If this is the case, they should also not be legally responsible and should not face the death penalty.