The closest thing we have to "Heroic Sociopathy", unlike true sociopaths (who lack a sense of right or wrong) these characters are so obsessed with protecting the world from evil that they become nearly single-minded and engage in methods that easily pushes them to the very edges of heroism (and often into outright villainy). Some particularly zealous heroes take the fight against evil to the next level. That is the Evil Exterminator. More than just killing the villain if pushed, Evil Exterminators deliberately set out to purge the world of some kind of evil, usually manifested in the form of an evil/hostile species of some kind, but also sometimes simply going out of one's way to rid the world of particularly corrupt/evil individuals, such as criminals.
For obvious reasons this tends to be seen as rather ruthless behavior, and heroes who indulge in it can very easily end up in Anti-Hero territory unless the victims are particularly evil or mindless creatures, a good example of the latter being Legolas from Lord of the Rings.
Evil Exterminators will do anything in their power to stop the spread of evil in their setting and can be seen as obsessed or even psychotic.. however if they willingly endanger innocents they are a Well-Intentioned Extremist villain.. the Evil Exterminator is, however, willing to fight and even harm other heroes if they get in their way of stopping injustice.