Is vaccination surgery? After all, you are physically manipulating the body, albeit in a very small way, to achieve a medical result.
What about getting a wart removed? Is that surgery?
Cutting.
So vaccination no, wart removal… maybe… if it were excised.
sewing up repairs are also.
Endoscopic examinations without cutting get called surgical.
Wikipedia’s got a pretty decent working definition. Let’s start there and quibble it to death:
As far as things like billing and scope of practice, a decent rule of thumb is to look for the suffixes. -otomy, -ostomy, -ectomy, -oplasty, and mostly -oscopy (except things like fluoroscopy) are generally considered surgical procedures that require and MD, OD, NP, PA or specially trained nurse or specialist to do, and a consent form to be signed before they do them. Surgical debridement (the cutting or scraping away of yucky stuff with a laser, scalpel or other bladed instrument to reveal a clean wound bed) doesn’t fit the suffixes, but it’s another one considered to be surgical.
As a very rough guide, if it involves something going inside the patient that isn’t a needle or simple tube, it’s probably surgery.
It’s surgery if no gentleman would perform it.
Surgery is manual labor, and gentlemen simply do not stoop to manual labor. Barbers, the common men they are, do manual labor, while gentleman physicians treat by diagnosing and prescribing on the basis of a case history and external appearances.
Of course, nowadays you needs must become a physician to practice as a surgeon, but that does not modify precedent. Therefore, in the UK and the Republic of Ireland, a man who becomes a surgeon will still be addressed as Mister, even if he holds an MD. Or, at least, is under certain circumstances, because it wouldn’t be a tradition without being bizarre, and it wouldn’t be a British and/or Irish tradition without being incomprehensibly ad-hoc and perverse. According to the Royal College of Surgeons, it gets better: The person starts out as Mr, Mrs, Miss, or Ms, becomes a Dr, and then becomes a Mr, Mrs, Ms, Miss once again after becoming qualified to practice surgery. And, of course, the President of the Royal College of Surgeons thinks that has gotten silly and they should stop it right now and call surgeons Doctors. And now you see why, across the pond, Dr Pepper punts the whole mess and goes by Sgt. Pepper.
Iirc, setting of broken bones was historically considered surgery, as it was a manual operation.
Historically, there were two areas of practice, medicine (aka physic) and surgery. Medicine included “diagnosing and prescribing on the basis of a case history and external appearances”, and would also have included talking therapy in the manner of a modern psychiatrist.
Surgery was hands-on work, such as setting bones, removing diseased body parts, etc.
[QUOTE=Geoffrey Chaucer, 14th century]
…
With us ther was a DOCTOUR OF PHISIK;
In al this world ne was ther noon hym lik,
To speke of phisik and of surgerye,
[/QUOTE]
How do you perform a surgical endoscopic examination without an incision? I have had a colonoscopy, an upper GI, and a cystoscopy, and as a patient I wouldn’t consider any of them surgical.
I have had both laser eye surgery and injections of drugs via a hypodermic needle into the eyeball. Both were called “eye surgery” (and were billed as such).
What about dentistry? Is drilling a tooth surgery? What about extracting one?
There are procedures in which tissue is frozen as a way of killing said tissue. It’s termed cryosurgery. No cutting.
My husband had lithotripsy for kidney stones and it was considered surgery.
Med records generally refer to these as surgical procedures. I also see various pain injections described as “surgeries.”
A surgery is any action that is recognized as surgery by surgeons.
(apologies to Mark Twain).
I’ve had a splinter removed from a finger by a physician (don’t ask) and it was billed to the insurance as “surgery”. I guess because it involved a tiny bit of cutting.
I wonder if in that case, it’s considered surgery because its predecessor (and current alternative) as a treatment for kidney stones was plainly surgical.
A tautology is a thing that is tautological.
I had an apicoectomy a couple years ago after a root canal failed, and the dentist always referred to it as “surgery”. I had nightmares before that procedure, which took about 10 minutes and was less traumatic than a filling.
It worked, too, because I still have the tooth. The dentist thought that procedure was going to fail, too, but it didn’t. 
It was a front incisor, so that was important to me.