Son of the architect Miguel Mieg, Juan began his training at the School of Arts and Crafts of Vitoria. He later moved to Barcelona to study Architecture, but once there he discovered his true passion for painting.

From his beginnings in Catalonia, Mieg was influenced by the concepts and working processes of the Surrealist movement and of Informalismo and soon entered into contact with the work of Antoni Tàpies (1923-2012)—who would exert a special influence on him— as well as Rafols Casamada (1923-2009), Joan-Josep Tharrats (1918-2001), Modest Cuixart (1925-2007), and Joan Miró (1893-1938). His interest in the avant-garde encouraged him to move to Paris for a time. In 1964 he settled in Madrid, sharing studies and experiences with his friend Carmelo Ortiz de Elgea at the studio of the artist Julián Gil (1939).

In 1966 he returned to the Basque Country and founded Orain, a group made up by Carmelo Ortiz de Elgea (1944), Jesús Echevarría (1916-2009), Joaquín Fraile (1930-1998) and Alberto Schommer (1928-2015), which connected with the movement of other artists in pursuit of the renewal of Basque art within the context of the burgeoning

 Basque School Movement 

a movement that emerged in 1966 in the Basque Country, consisting mainly of three different groups: Gaur (Today) from Gipuzkoa, Emen (Here) from Biscay and Orain (Now) from Alava. Promoted by the artists Agustín Ibarrola and Jorge Oteiza, the movement focused its activity on a defence of Basque avant-garde art. The collective was soon affected by internal disagreements that ended in its disbandment in the same year it had been created.

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Mieg had his first solo exhibition at Galería Mikeldi in the 1970s. In the 1980s, his painting incorporated a number of planes and graphic motifs, taking ’s interpretation of space as his reference, and ever since then his practice underwent a progressive evolution.

Mieg has exhibited his work in many galleries and museums, mostly in the Basque Country.