哆 almost never appears alone — its main job is in the disyllabic word 哆嗦 (duōsuo), 'to tremble; shiver from cold or fear'. The character is also used phonetically in transliterations: 哆啦A梦 (Doraemon), and as the solfège syllable 'do' (哆来咪 do-re-mi).
memory
口 (mouth) on the left + 多 (many) on the right — picture chattering teeth: a mouth that 'multiplies' its sound when shivering. The shivering meaning is reinforced by the doubled 多 → many small movements.
The mouth radical on the left tags 哆 as a vocalisation — used in 哆嗦 to tremble (the chattering of teeth) and as a phonetic syllable in transliterations like 哆啦A梦 Doraemon. Mouth-radical onomatopoeia includes 哈 ha, 喔 oh, 呀 ya, 呢 ne.
多 supplies the sound duō unchanged — a clean phonetic tag. 多 itself is two 夕 (evening) stacked, originally suggesting many nights piled together; here only the syllable is borrowed, not the meaning. Same phonetic family: 移 move, 够 enough.