Title text: Some personal news: After treating my first case a few years ago with antibiotics, I can report that I have now had appendicitis for the second and--unless something extremely unexpected happened with the surgery--final time.
In normal medicine, appendectomy is the surgical removal of an appendix. The purpose of the appendix is not fully understood, believed to be a reservoir for a human's gut microbiome. However if an appendix is swelling, it comes with risk of bursting and causing massive damage through internal bleeding and septic bacterial infection. In such cases the appendix may be partially removed through surgery.
Breaking down the comic's title: circum- means "around," -appendiceal means "the appendix," som(a)- means "the body," and -ectomy means "removal." Therefore, a circumappendiceal somectomy would be "a removal of the body from around the appendix." This appears to be the procedure that the doctor in the comic is describing.
The joke is that such a procedure is functionally identical to a typical appendectomy, the removal of the appendix from the body - just viewed from a different perspective. It humorously implies that the entire body of the patient is the problematic part to be removed, leaving the appendix behind. It should be noted, though, that the procedure is identical only if it's done without disrupting the integrity of the body. There are situations in which an essential part is removed from a damaged or unimportant system by dismantling the system, piece by piece, leaving the part behind. Obviously, this would not be an advisable method for treating appendicitis. 
The title text provides personal insight into the comic. It appears Randall has gotten appendicitis before, which may have been the inspiration of 2147: Appendicitis and was treated using antibiotics instead of surgery. However, his appendix became inflamed again, and this time it was removed. Randall's experience is not uncommon, as a 2020 study found that nearly 40% of patients treated with antibiotics for appendicitis required an appendectomy for recurrent appendicitis within 7 years. However, this should be the final time, as it is unlikely to get appendicitis without an appendix. However, he does not rule out the possibility that something "extremely unexpected" happened during the surgery which could cause him to suffer from appendicitis again. Possible candidates for such an extremely unexpected event could include the surgeon faking the removal of Randall's appendix and leaving it intact, or removing only part of it, removing Randall's appendix but transplanting someone else's appendix into him instead, or even the appendix's spontaneous regeneration. While most of these possibilities are absurd, stump appendicitis, in which appendicitis occurs in remnant of the appendix that remains after surgery really does occur in 1 in 50,000 cases according to the article Appendicitis after appendicectomy - NCBI.
- [Cueball is sitting with legs out over the edge of an examination table, hugging his stomach, likely because of stomach pains. A doctor in lab coat and a surgical head cap is standing next to the table speaking to Cueball, one arm stretched out towards him.]
- Doctor: Normally we would remove your appendix from your body.
- Doctor: But thanks to new surgical techniques, we're now able to remove your entire body from around your appendix!
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Please please please leave in the  after "it is unlikely to get appendicitis without an appendix" :) 18.104.22.168 01:29, 28 August 2021 (UTC)
- Sure - this time Randall is even himself uncertain! ;-) --Kynde (talk) 09:01, 28 August 2021 (UTC)
- Hey, but we've already got a citation (reference to a science paper in the last sentence of the explanation) -- 22.214.171.124 11:05, 30 August 2021 (UTC)
Removing the body around an appendix? That's easy, I can do that. Someone just point me to where the appendix is and how it looks and I'll cut away everything around it. Also, it sounds like the consciousness would remain in the appendix, which would likely not be very comfortable. Fabian42 (talk) 12:42, 28 August 2021 (UTC)
- That reminds me of the apocryphal quote by Michaelangelo, that he got a big block of marble and chipped away everything that didn't look like David. Barmar (talk) 13:03, 28 August 2021 (UTC)
- I considered making that same reference (except that I didn't know who said it), but the final argument against it was that I couldn't find the correct term for that art form, so I couldn't say what I was talking about. In German it's "Bildhauerei". All the translation websites only give me "sculpture", but I'm trying to talk about the process, not the product. Fabian42 (talk) 16:44, 28 August 2021 (UTC)
- That would be "Sculpting" --126.96.36.199 17:36, 28 August 2021 (UTC)
- Or possibly, "subtractive sculpture", which pares away, to differentiate from "additive sculpture", which builds up. --188.8.131.52 22:00, 31 August 2021 (UTC)
- Yes: While theoretically, removing body from appendix and removing appendix from body are just two description of same thing, practically there is difference in which part is supposed to remain functional afterwards: removing body from around the appendix may result in the body ending up in multiple pieces. -- Hkmaly (talk) 01:55, 29 August 2021 (UTC)
- We should really have a medicine category, for all the medical comics, like this one. 184.108.40.206 06:30, 29 August 2021 (UTC)
- Good idea! --GcGYSF(asterisk)P(vertical line)e (talk) 07:31, 29 August 2021 (UTC)
- Yes, could be a good idea, but should is just be called Medicine? Is there some other better name? Healthcare or something? Medicine sound just like the pills you would get from the doctor, but maybe that is just because I'm not native English speaker. Also which comics to include? There could be many, but as for instance with a category for spiders, there is no easy way to search for those that should be included in this new category. Please feel free to add examples here below (oh and how many of the covid comics would be about medicine? Not all I guess so cannot just add that category).)--Kynde (talk) 09:40, 30 August 2021 (UTC)
- The Category:Doctor Ponytail category should be a subcategory of this category, and others include 938: T-Cells, 830: Genetic Analysis, 644: Surgery, 738: Incision, 746: Birth, 431: Delivery, 1619: Watson Medical Algorithm, etc. Perhaps it could be called healthcare? These are medical / doctor related comics. 220.127.116.11 18:28, 30 August 2021 (UTC)
Reminds me this Dilbert comic: https://dilbert.com/strip/2005-05-23. Replacing all of your parts isn't difficult if you do them all at once. Shamino (talk) 16:10, 29 August 2021 (UTC)
There's a parallel to head transplants, which are now called body transplants because the idea of transplanting heads apparently grosses people out. 18.104.22.168 16:13, 31 August 2021 (UTC)