sleep, die, sleepy
眠 centers on the state of being asleep or drowsy. The 'die' sense is a euphemistic extension, likening death to a final sleep.
眠 combines 目 (eye) with 民, which likely contributes the sound and may suggest closing or covering, as in the eyes closing in sleep.
The eye radical 目 beside 民 suggests eyes that are closed or heavy. Picture your eyes slowly shutting as sleep takes over.
For ミン, imagine a person sleeping so deeply they don't notice the mint leaves falling on their closed eyes: mint -> ミン.
to sleep
sleep
sleepy; drowsy; somnolent
sleep; sleeping
hypnosis
sleeping; asleep; resting; slumbering
sleepiness; drowsiness
nodding off (while sitting); dozing
sleeping pill; sleep medication
nap; doze
hibernation; winter sleep; brumation; torpor
sleeplessness; insomnia; wakefulness
dormancy; quiescence; diapause
sleeplessness; insomnia; wakefulness
sound sleep; good sleep; quiet sleep
sleepy; drowsy
eternal sleep; eternal rest; passing away; death
pleasant sleep; good sleep; sleeping well
to put to sleep
idle slumber