Most people think that "surgery" is a procedure done with a knife. Actually, according to Dorland's Medical Dictionary, 26th Edition [Dorland26], surgery is "that branch of medicine which treats diseases, injuries, and deformities by manual or operative methods."
Dorland's also gives the history of the word as being derived from the Greek words cheir (hand) + ergon (work). Thus, the foundational meaning of "surgery" is any procedure done using the doctor's hands - possibly holding a knife, but also possibly holding an "Activator" tool or doing massage or Chiropractic work. Indeed, the word chiropractic also derives from the same Greek word cheir (hand) + prattein (to do).
Word games aside, Naturopathic Medical Doctors (NMD) in some states (including Arizona) are authorized by law as a part of their scope of practice to use (hand-held) knives (scalpels) and similar devices to make "minor" cuts on their patients, for example to remove a wart or do an "incision and drainage" procedure.
While the definition of "minor" surgery varies by state, in Arizona it is generally understood to include any procedure that does not require general anesthesia or require opening the body cavity, so long as the naturopathic medical doctor is properly trained to do the procedure.