OP - you seem rather dismissive of your DD's work and struggles, you say she "walked" into a graduate job 3 years ago. No, she didn't, no one just 'walked' into a graduate job in 2010/11, she faced stiff competition and will have had to work bloody hard (unless she's very gifted) in order to keep it.
Was your DS equally dismissive at the time? Did he take the piss at all of her working hard, her job, her pushing herself at that time? That doesn't mean she can't be kind now, but if he was in any way taking the piss at her back then, it could be she's gloating a bit due to an attitude of "see, this is what I was trying to avoid". Or does she think he didn't make the most of chances he had? Did she make sure she had a good CV with extra curricular activities and work experience whereas he was lazier? did she try to give him advise he poo-poohed at uni stage? Or did he mouth off about his future career (which has obviously not panned out).
"another week in job paradise" and comments about filling filing cabinets doesn't sound that much of massive insult, seems rather tame to me (normal sibling banter for our family and for DH's), his reaction however, is rather extreme.
I would talk to her like an adult and say that joking aside, you are genuinely worried about your DS's mental health, he's not coping well and could she suggest ways to help him? That you wondered that as her experience is so much more recent, could she talk to him seriously about what he does next career wise.
If she has previously been close to him, and this is out of character, there must be something going on. You seem to see it as her just being a bitch for no good reason, find out the reasons before you destroy your relationship with your DD.
If you ban her from your house, don't expect her to want to come back when you decide to lift your ban.