This is an old Christian debate - as, as usual, the answer depends on metaphysical assumptions.
There is a traditional and respectable Christian argument that there cannot be pure evil, because evil is essentially the lack or 'privation' of good. This (strange) conclusion arises from the metaphysical assumption that God created everything, from nothing (ex nihilo); and God is wholly good; therefore everything that is - is good in an ultimate sense.
By this account evil is a misguided good. An example would be Adolf Hitler, who seems (when committing his greatest atrocities) to have sincerely believed (most of the time, anyway) he was doing good according to his own ideas of good.
To go further, by this account evil is a kind of insanity. People are simply irrational to suppose that they can oppose God; because, as they themselves are wholly elements of God's creation, they have no basis for opposing God's creation.
Therefore - from such metaphysical assumptions - there cannot be 'pure evil'.
However, the Mormon Christian metaphysics allows for real evil, 'pure evil' - evil for its own sake.
God created from pre-existent stuff; and men were, in some essence, co-eternal with God - therefore Men can genuinely oppose God's creation from that part of them that was not created by God.
From such assumptions (which I personally hold) it is therefore possible to do pure evil; by purely opposing God's creation without any attempt to aid creation or any created entity - indeed to attack creation at the cost of expending effort, and indeed at the cost of one's own happiness, health, and life.
By this account the purest evil is not really such epic and infamous inflictors of human suffering such as Hitler - but spitefulness, and related sins such as envy and resentment.
This is the infliction of harm for the sake of inflicting harm - a child breaking another child's beloved toy; an internet troll writing something intended to annoy or wound; someone who says or does things specifically in order to 'wind-up' another person; or a political leader who acts to induce spite, resentment and envy in the population.
Thus pure evil is something of which many, indeed most, people are guilty. And the most evil public figures are not those who cause the most death and destruction - but those who systematically stir-up spite, resentment and envy.