The psychiatrist is liable but so is the surgeon, just as if he had performed liposuction on an anorexic. ...or removed a lower leg, a hand, and an eye from a child who believed he was a pirate.
That the teenager's parent signed off on it just means that the hospital staff should have called protective services.
Children cannot consent to mutilation and sterilization. If their parent signs off on it, that's evidence to be used to take the child away from them and that the parent should be institutionalized.
In some cases, if the parent does not consent, the child can be forcibly removed, and the parents arrested for child abuse, after which the procedure is done. If the doctor does not recommend or is unwilling to perform such a barbaric procedure, they can lose their job, license to practice medicine, and be sued into bankruptcy.
If a cancer specialist diagnoses a patient with kidney cancer and recommends the removal of one kidney, I don’t see how the surgeon who does the procedure would be liable if it turns out that the cancer diagnosis was incorrect.