Does your hear beat speed up or slow down in natural death

It depends on what has caused the death. If by "natural death" you mean dying of old age, the chances are it would slow to a stop. But "Natural" simply means it wasn't caused by an outside source (i.e. a wound, impact, etc.) For example, someone could die "naturally" after suffering from tachycardia.

Tachycardia happens when the electrical current that keeps the heart pumping steadily goes out of whack and goes too quickly. This can lead to a myocardial infarction (heart attack), a stroke, sudden cardiac arrest, and unfortunately, death.

It slows down