What are the long term effects of killing off a main character (early into a series) that represents someone you'd like to move on from? Would that be cathartic, or detrimental to a writer?
At this current moment in your writing process, your world and its characters are vibrantly real to you and completely unknown to your future readers. So this is a wonderful time to use your story for a little self-indulgent soul surgery. If you need to strike out at someone in the real world, put their representative character through the ringer in your fictional world. Drag them literally through the proverbial dirt, then crucify them on a cross of your creativity. Vent your rage, your disappointment and your pain out onto the page and let your emotions rule your writing for a few hours.` Don't just slash them off the page in a single sentence. Fill paragraphs with their punishment and pages with their demise.
Then, when you are feeling a little better, carefully select the "Save As" option in your word processor and name this new document, TheDeathOf___.doc. That way it doesn't overwrite your existing work in progress, but it does preserve these valuable new pages for future review.
Tomorrow, or next month, when you are feeling in balance again, read through tonight's creation and notice how your emotions shaped your words. Study the raw creation, looking for rage-inspired explicates and other venomous prose. These may well be the most honest words you write this year (which is okay because you are a fiction writer. You are supposed to lie.), but if you look carefully at these words after your emotions have cooled, you will probably also find that they are real in many ways that your normal writing is not. Learn from them and thus become a better writer.
Never pass on an opportunity to write while angry or sad, in love or out. Write all the time and write with energy and passion. Write without regard for whether your future fans will ever read your latest words. Not every word which you write should be destined for publication. Most of them, should just be you, practicing and learning how to better tell your tales.
While I agree with @Henry Taylor, I would also like to add it may depend. I find that writing such pieces may be cathartic only if well done (at least for some people).
An example: Bobby is a bully (and represents all the bullies that made my life hell) so I make him act as despicable as possible, then I have Tommy take issue with him and give him a gruesome lesson. This satisfies my need for revenge and I feel vindicated... for a while. Sooner or later, a new Bobby will emerge in my writings and I will again feel the need to make him suffer.
This becomes a vicious circle and, if I can't break away from it, then there isn't much catharses in the writing for me as a writer, is there?
What I found was the most cathartic for me as a writer was writing these Bobby characters from their POV (at least on occasional chapters) and giving them a rich personality. Making them more human and less villain. Trying to understand what was behind their actions (without falling into the trap of always giving them a hellish life at home, even though that reason may apply to some bullies in real life).
Then I'd look into trying to have my MC search for ways to fight and overcome the bullying.
I found that it was the combination of understanding my foe and searching for natural ways of defeating them that brought on the much desired feeling of catharses.
But if you're writing a mystery and your killer is aiming at bullies, that's a different story. However, the killing itself is probably not going to be cathartic in the long run, but rather how the killer evolves (for the writer also evolves with the MC in some ways) and learns different ways of dealing with the difficulty.
Of course some people will find a deserved savage death to be cathartic, and it may very well be the case. But if one finds the need to dish out these deaths to the same characters over and over, then it's not cathartic at all.
A particularly interesting account if you can find it is found in Dragonlance: the Annotated Chronicles, by Margaret Weis and Tracy Hickman. They killed off one of their particularly main characters, and in the annotations they talked about how it was a particularly painful thing to do - there were many tears shed in the writing of that scene.
Personally, there were many tears shed in the reading of that scene, as well.
When I began writing my first novel I was very angry. I killed 11 people - I feel a lot better now.
The book didn't sell but by writing it I saved spending thousands of dollars in therapy . . . so I'd call it a win definitely.
More seriously . . . your plot dictates that certain people have to die. Pure hatred causes the mind to create ways to inflict extreme suffering on your villains.
For my first killing was a little tentative. A girl watches as her boyfriend chokes on a chicken bone and makes a conscious decision to nothing.
It's all learning. I could say, my first few killings were for me . . . but now I'm really good at it. I've had a character express the joy of being blown up on 9/11. No . . . I'm not joking.
Just so as I don't get marked down for bad taste.
When the moment came? Wow! The last rush. Like a breaking tidal wave; our maker came calling. With a violent crash he reached into our world. Then he took us. What a sensation! What a ride! There was no feeling of pain, only a craving for the exponential growth of the infinitesimal moment, no sensation of falling to doom. Our worlds moved with us in a triumphant cascade. And there was music, blissful music. Katrina came into my heart and together we surfed on the crest of a magical wave of a million tons of beautiful concrete and steel. And we flew as kites on a magical wind. And we danced our last dances and sang our last songs. And we embraced one last time. And we laughed out loud. We laughed our loudest, and our joy could be heard above the twisting of steel and the breaking of glass. For all time our laughter would echo in this place, on this wave, to be carried forever on the magical wind, in this precious last moment of goodbye. At last we were again, and forever together, as children.