Three-drops water radical on the left, the side form of 水. It carries the meaning: rinsing the mouth and gargling are water actions, so the radical does direct semantic work, placing 漱 in the wet-mouth family along with 涕 tears, 涎 saliva, 洗 wash.
The right side 欶 supplies the sound, shuò drifting to shù through a regular vowel shift. 欶 itself combines 束 bundle with 欠 mouth-open, depicting sharp inhalation. A faint semantic flavor leaks in: gargling is a mouth motion involving water moved by breath, so the phonetic indirectly reinforces the picture.
