The title of Mikan's execution is "Bye Bye Ouchies" or "Pain, Pain, Go Away."
It's a chant that gives strength to children when they're in pain, almost like magic.
Nipmikanfag made the interesting comment that this gave him the mental image of a Mikan who is shut up so tightly inside, crying out for all the abuse to simply stop as she is executed. Therefore it could be something Mikan used herself as a kid as a survival mantra which is sad because for all those times it somehow worked in the past, as she is executed, it didn't. (Fuck DR3 for spoiling this)
I also believe that it can be interpreted as Mikan believing she is delivering Ibuki and Hiyoko from the pain of being separated from Junko by life by them joining her in death. From what is shown in DR3, Mikan might have felt that she was closest to Junko barring Mukuro so believed in her "better-judgement" to understand Junko's wish best, which was used for her to mentally accept her murder of them both.
It's also pretty despairing for a member of SHSL Despair to kill other groupies.
 Asphyxiating Ibuki and slicing Hiyoko's throat could be an emphatic statement against her bullies in general even if it's incidentally /them/ she killed. It's a statement that says, cease this endless chatter about nothing and listen to me. Because Hiyoko and Ibuki love to gab.
Another interesting note is that she has the body of a developed woman but the mental state of a child. Hiyoko has the body of a child and the mental state of one too (who may be jealous of Mikan's body.) When she "grows up" her mental state mellows out with this change which might imply that her childish form was one of her reasons for being crabby, Mikan is still stuck. (It's a shame they had little interactions that really confront the core of their conflict with each other but that's something that fanwork could explore. Especially as being different trajectories of victims of the same mistreatment.)
 The pleas that she makes for her bullying to stop are the kinds of bargaining children use to try to stop pain. None of these techniques worked which is why she didn't develop stronger ones for defending herself.
Next is my headcanon:
I believe that Mikan is a very tactile person who enjoys the pleasure of surgery and being touched in general if she calms down. Fear heightens her senses, which grounds her in reality and sexual pleasure disassociates her from reality. Sex sort of phases you into a weird state of being.
Shifting from two different worlds with no friends to ground her in reality has made her a romantic person who clings deeply to the ideal of love as redemption. Even an evil act has redeeming qualities if it's out of love and love redeems all. (Mikan reads a fair amount so of course she would love this concept.)
Mikan has stated in certain dangan island responses that she loves to read when she wants to escape reality. Not always disgusting books full of parasites where she fantasizes about the pain it inflicts on the victim but different narratives. She also has read some of Touko's books and enjoyed them in an adorable TDP interaction. On Jabberwock Island with Hajime by her side in the library, she's enjoying the time so much that she doesn't for once, want to escape because she wants to experience the reality of right now. Awwwww!
Some final words are, Mikan is not the kind of character who can simply be judged as pure or impure, Mikan simply is. You can call her a stupid slut if you want, but by doing so, you are ignoring the most fragile parts of her humanity, couched in impurity. By digging through many confusing mixed messages you can find the loving woman who is simply seeking love. Thanks for reading.