Hand radical - 扌 is 手 (hand) in left-side form. 搞 is the all-purpose 'do/handle/mess with' verb, so a hand radical fits perfectly. Joins the huge hand-action family: 打 (hit), 拿 (take), 拉 (pull), 推 (push), where the hand on the left labels the character as an active manual verb.
Right component supplies the sound, gāo to gǎo, tone shift only. 高 is itself a pictograph of a tall watchtower. As a phonetic it also feeds 稿 (manuscript/draft) and 镐 (pickaxe), all keeping the gao-rime - a clean little phonetic series.
