What does general anesthetic do to stop your heart?

They dont: General anesthesia does not stop the beating of a patients heart unless given in an extreme over dose the same way most any medicine would. General anesthesia works at the level of the brain to impede memory production and muffles the bodies outflow of adrenaline during the stress of surgery.

Nothing: Unless you have an allergic reaction or electrolyte imbalance with one of the anesthetic drugs, which would be readily detected by your provider, it is very unlikely that an anesthetic would stop your heart. People can get into trouble if they have a large drop in blood pressure which can decrease perfusion of the heart via the coronaries. This can put your heart at risk.