Bottom 目 is the indexing eye radical, a vertical eye-frame with horizontal lines for iris and pupil. Marks 督 as an act of watching: supervision is fundamentally vision-with-authority. Same radical family: 看 (look), 眼 (eye), 睡 (sleep), 盯 (stare).
Top 叔 supplies the sound, shū drifting to dū through an Old Chinese velar-cluster split, the same shift seen in 督促 (urge). Pure phonetic loan; the 'uncle' meaning of 叔 contributes nothing.
