A person who manipulates puppets, especially in traditional Japanese puppet theater (ningyō jōruri) or similar performances.
He is a famous puppeteer who performs on the bunraku stage.
人形遣い is a more common term for a puppeteer, while 操り人形師 emphasizes the manipulation aspect and may sound slightly more formal or literary.
Compound of 操り (ayatsuri, 'manipulation') + 人形 (ningyō, 'puppet') + 師 (shi, 'master' or 'specialist').