Born in 1226 in Qingyuan Prefecture (modern Ningbo), Song China. Ordained at thirteen, he trained widely. When Yuan soldiers invaded and held a blade to his neck at Nōninji temple, he reportedly rebuked them — "Do not trouble yourself" — and continued meditating. In 1279 he came to Japan at the invitation of Hōjō Tokimune and entered Kenchōji. In 1282, Tokimune founded Engakuji to console the dead of the Mongol invasions and installed Mugaku as founding abbot. He became Tokimune's spiritual pillar during the national crisis. He died in 1286 and received the title Bukkō Kokushi.

A man of courage transcending life and death. The "Do not trouble yourself" episode before Yuan soldiers' blades symbolizes his unshakable composure. He served as the spiritual backbone for Tokimune and Kamakura's warriors facing the Mongol crisis.

Engakuji flourished as the second-ranked temple of the Kamakura Five Mountains and remains the head temple of the Rinzai Engakuji school. His dharma lineage continued through Kōhō Kennichi and Musō Soseki, profoundly influencing Muromachi-era Five Mountains literature and culture.