To a person who has lost a pet during a surgical procedure, the risks will seem higher than they really are. I understand that....it is horrible to lose a beloved pet.
The fact remains that losing a pup due to anesthesia is very low.
From the following link:
01 Is Anesthesia Safe? - VeterinaryPartner.com - a VIN company!)
Modern anesthesia is very safe. The risk of a pet dying under anesthesia is less than 1%. The rare patients that are lost under anesthesia are generally emergency surgeries, when the patient's condition is extremely critical. The risk of a pet dying under anesthesia while undergoing a routine spay, neuter, dental or mass removal is extremely low, but this risk can be affected by the anesthetic drugs used and the monitoring of the patient.
Of note; IMHO I believe the monitoring of the patient is the numero uno issue. Some vets may shortcut on this and that can be dangerous. One person should be in charge of monitoring a patient the entire time to check heart rate, blood pressure, temperature, oxygen levels and well being.