There's no such thing as senseless violence, according to the one who commits it. Characters who kill or torture without at least an internal justification are crazy, not evil. You don't have a reason to kill people in the party or at random, so you don't. This doesn't make you nonevil.
Also remember that just because you're Evil doesn't mean you're a villain. Many Evil characters have no ambitions higher than their own survival and/or comfort; they don't aspire to great power, nor to purge the world of the target of their hate. They're just trying to get by, not so different from the rest of us.
The traditional list of Seven Deadly Sins was originally compiled not so much as a list of inherent sins, but a list of reasons that people sin. This makes it a great source of motives for Evil characters. I prefer to expand the list to nine, adding Fear as Wrath's twin in the fight-or-flight reflex, and Despair because it was actually in the original list; Sloth replaced it later.
Avarice: The key to happiness is having things. I will have it all.
Envy: I deserve it, not them. I will have it from them.
Gluttony: Pity those not at the top of the food chain. I will never be in that position.
Lust: I want to do it all, and I will let nothing get in my way.
Pride: I must be better then them: so much so that my superiority is never even questioned.
Sloth: I just don't want to do it. Let them do it for me. If they refuse, make them do it for me.
Wrath: They will never hurt me again. I will punish them for what they did, and leave them unable to do it to anyone else.
Fear: They must not be allowed to hurt me. (Note the lack of an again here: this is one of the big differentiators between Fear and Wrath, but it can make a huge difference in the character).
Despair: I just want the pain to end. Giving it to others helps.
Also keep in mind that these are core motivations. Any one of them will need to be elaborated upon. What is it? Who are they? How does the character plan to achieve this goal? Also worth noting is the lengths that your character goes to to hide her motives. Evil characters often prey upon one another's weaknesses, and while Wrath-type characters might not worry about seeming weak due to their motives, Sloth-type and Fear-type characters likely would. These folks are likely to construct a facade, often but not always based on Wrath, as a matter of posturing.
Your character sounds like a Wrath-type, with a focus on the undead. Because her main focus is on something that is not so amenable to the survival of humanity in general, she can get along decently well in society, and even be a very useful sort of person to have around. Some might even mistake her for heroic. But she has a twisted fight-or-flight reflex: any slight or injury, real or imagined, runs the risk of touching on that trauma, for reasons that make sense only to your character (if they even make sense to her). She might lash out disproportionately at small threats, or even against things she mistakenly believes to be threats, but are not.
Best Answer
It takes some discipline, but develop and use fake profanity, specific to the setting. You have an advantage here, as the GM (which I infer, since this is about an NPC, not a PC) because it is perfectly within your purview to simply say, "These phrases are mild blasphemies, these ones are mid-range vulgarities, and this one here is fightin' words." Your other NPCs can react appropriately, too.
An excellent written example of this is in Robert Jordan's "Wheel of Time" where, expressions like "blood and ashes!" or "bloody flaming ashes!" are understood to be at least mid-level adult vulgarities in the setting-- used by one character in particular, to the vast disapproval of several others.
But it works in games, too: In in Amber game I'm in, a Rebman character has a fairly extensive catalog of fishy metaphors as vulgarities. They're not vulgar in English, and probably not in Amber, but they are in Rebma, by my understanding.
It should be pretty easy to adapt this to a typical game setting.
As an afterthought, this might be an example of what you mean by a list of "clean insults." If so, I will add only that in my experience, the list doesn't need to be that long, if it's evocative.
Possibly worth noting that I take a different approach with my character in the same game: He is also known to be able to strip paint and turn the air blue, but rather than using my own extensive talents in that direction, I'll often just describe him as saying something presumptively foul in his native, non-Thari language. If NPCs or PCs who understand the language are in the same scene, they'll sometimes react appropriately, if they are easily offended.