Why is it that when I vomit it feels like my heart stops?

Vagal reaction. The stomach is controlled by the vagus nerve. This nerve is a parasympathetic nerve. Parasympathetic nerves release acetylcholine which can cause the heart to slow down. Severe vagal reactions can cause the wart to slow enough that you can pass out from lack of sufficient blood pressure.
Vagal reaction. When you vomit, it may cause a surge of the vagus nerve, which can slow down the heart. That may be the reason. But, if this happens often, you should definitely see your doctor.
Interesting. In general, the only way you would feel your heart had stopped, would be that you were resusitated and later told it had stopped! curiously though, retching and vomitting are associated with increased activity of the vagus nerve which causes the heart rate to slow down. Some people are more sensitive to this. Must be frightening to experience!