The title Cutting for Stone is a pretty on the nose, but it can take a while to figure it out if you're not a doctor who's memorized the Hippocratic oath. That's the professional promise that doctors make ("first do no harm") when they first become legit doctors, and one of its vows goes a little like this:
"I will not cut for stone, even for patients in whom the disease is manifest; I will leave this operation to be performed by practitioners, specialists in this art…" (Part 3, epigraph)
Wait, what? Okay, let's slow down. According to the author, this refers to back in the day when people got lots of bladder stones, and so there were lots of dudes who went around cutting them out. Problem was, these dudes didn't know much of anything about germs and bacteria and things like that, so lots of people got infected. This promise is basically a repetition of "do no harm"—it's just more specific.
It also fits handily in with the surname of many of the characters: Stone. Dr. Thomas Stone, Shiva and Marion Stone's biological father, abandons them on the day that they're born. They spend their lives wondering about him; his memory, or lack thereof, bugs them. When Marion finally gets the chance to find him he digs in, almost surgically extracting an apology from his dad. Get it? Deep, right?