SapphireFox<3

Here's the Hebrew word מוּת - die (as translated in the passage)

Strong’s Definitions מוּת mûwth, mooth; a primitive root; to die (literally or figuratively); causatively, to kill:—× at all, × crying, (be) dead (body, man, one), (put to, worthy of) death, destroy(-er), (cause to, be like to, must) die, kill, necro(-mancer), × must needs, slay, × surely, × very suddenly, × in (no) wise.

So.. Why is your interpretation correct?

The Hebrew is, literally, die-die (muwth-muwth) with two different verb tenses (dying and die), which can be translated as “surely die” or “dying you shall die.” This indicates the beginning of dying, an ingressive sense, which finally culminates with death.

muwth