mī is the squinting reading, as in 眯缝 (to squint narrowly) and 眯眯眼 (slitted eyes); it also colloquially means to take a short nap. A separate reading mí means to get something in the eye.
目 on the left is an eye stood on its end, pupil framed by lid lines. It indexes 眯 in the eye family with 看 to look, 睡 to sleep, 瞎 blind, marking it as something the eyes do.
米 on the right supplies the sound with a tone shift, mǐ to mī. It also adds a faint image: a tiny grain is exactly the kind of speck that gets in an eye. Same phonetic appears in 迷 lost and 谜 riddle.
