Honestly, I wouldn't want to kill ANYBODY from the mario series. Every major character has some importance to the series and it wouldn't be the same if they were gone just like that.
Mario: Well, obviously he needs to stay, he's the most famous game icon in the world. (I hope that's right...)
Luigi: Infamous Mario's brother, need I say more?
Peach: Damsel in distress, and always will be but she's been in the series too long to be removed. Plus, she's known for being an infamous damsel in distress and who could do it better?
Daisy: She is best friends with Peach, and I'm guessing known to be Luigi's girlfriend. Mario saved her in a game, and she's been in almost every spin-off game plus she'll always be known for being a tomboy, but I'm pretty sure that's what many people like about her.
Yoshi: Been in the series since the beginning basically and I think Yoshi has more fans than Mario so if they kill him off, many fans wouldn't even look at another new mario game again.
Birdo: Her gender complexity is probably what made her so famous. Not to mention, it's pretty much assumed that she is Yoshi's girlfriend so since people love Yoshi really a lot, they would notice Birdo as well.
Toad: Been there since the beginning as well...well, almost. He's remembered for his infamous quote: "The princess is another castle!" and I'm guessing he's a servant of some sort to Peach? He's been in almost every game since Super Mario Bros.
Donkey Kong: Again, been in the series since the beginning with Mario's very first game. Plus, he's the star of the DK series so killing him off might bring some fans down. Very down.
Toadette: Okay, she hasn't appeared in many games, but her cheery and bright nature and attitude makes me like her a lot. Also, she is Toad' sister (that's what mariowiki on her says) and Toad is very famous as well so many more people could notice her. Killing her off would make me very sad.
Diddy: The second biggest star of the DK series. In my opinion, he definitely should star in more Mario games, cause he's got more speed and more of a humble nature than DK plus, imagine Diddy in a Mario adventure game where he is playable (Like Super Mario Galaxy) I think it would be very fun! Killing him off is a huge NO NO.
Dixie: Alright, she's not really THAT important to the Mario series, but come on I think she has HUGE potential as a regular Mario character! And I think she deserves more popularity and recognition cause I really do like her. Killing her off is also a huge no no. She is Diddy's girlfriend, who would Diddy be with when Dixie's gone? Tiny? It just wouldn't be and feel the same.
Rosalina: Definitely see her as a recurring Mario character. She's made too huge of a debut to be killed off already.
Bowser: The infamous villian of the Mario series. Many fans will be torn if they see that Bowser is gone forever. Who will replace him anyway?
Bowser Jr: Ehh, I don't know about him. But, I think he's already known to be Bowser's evil helper so killing him off wouldn't feel right.
Toadsworth: I actually don't even care if he's killed off or not...I never paid attention to him that much. But I'm guessing he'll stick around for a while cause he's known as Peach's caretaker...I think.