i think it would be hard to argue that the death penalty is intrinsically good, because it lowers the state to the level of murderer. It's not instrumentally good because research suggests that the very fact of the death penalty alters the behaviour of the juries asked to consider it. Many will stop short of a guilty verdict if the death penalty is on the table. However, psychological authoritarian followers will push very hard for the death penalty if it's on the table at all.
In addition, and related to Simon van der Longen's comment, the fact of the death penalty means that anyone committing a crime for which the death penalty is a possibility is immediatelty less constrained against killing potential witnesses because they are already in the position of potentially paying the ultimate price, so, getting rid of witnesses makes sense. As such, the death penalty, in certain cases is the opposite of a deterrent. Which seems to suggest that it is instrumentally (very) bad in some cases.
I suggest, therefore, that the death penalty is an example of an "evil" punishment.