José Mª Acuña López was deaf and mute from birth. He studied at St Fernando School of Fine Arts and taught modelling and sculpture at the School of Deaf-mutes in Santiago.
José Mª Acuña participated in many exhibitions such as the exhibition of Galician art in the Retiro in Madrid (1925), the one celebrated in Santiago in 1926 and the one celebrated in the International Gallery of Deaf and Mute Artists that same year. He also participated in the Biennials of Pontevedra (1972 and 1975) and exhibited his works in the Circle of Fine Arts of Madrid as well as in several galleries in Madrid, Vigo and Santiago.
José Mª Acuña was the author of the pilgrim fighting against the wind in O Cebreiro (Lugo). He was awarded Castelao Medal in 1991.