Born in Lima, Juan Acevedo studied at the art department of the National University of San Marcos and at the School of Plastic Arts of the Pontificia Universidad Católica del Perú. He started his career with 'Manuelito' in Informe Ilustrado in 1969-70. During the early 1970s, he contributed to Caretas, Oiga and La Crónica. He created stories and series like 'El Doctor Domingo Siesta, Cretino Colegiado' in Expreso (1974-75) and 'Samuel y Cervantes, los Geniecillos Dominicales' in the Sunday supplement of El Comercio (1977). Acevedo created the political 'Pobre Diablo!', worked on 'Comité Divertido' in Monos y Monadas (1978-82) and was art director of Collera (1978-79). Since 1975, he was also active as a teacher in Villa El Salvador.
In November 1979, he published the first episode of 'El Cuy' in La Calle. 'El Cuy' as a daily comic strip from 1980 to 1983 for the left wing journal El Diario de Marka. Acevedo was very prolific in the eighties with some comics done in the underground tradition. Following 'Pobre Diablo' he began a cycle of short lived bizarre characters like 'Guachiman' (last months of 1981 and the beginning of 1982), 'Orateman' (1982), 'Anotherman' (1986) and 'Trann' (1987). In the nineties he was specially devoted to his project of telling the whole story of Latin America for kids which was financed by a Scandinavian publishing house. In addition, he began drawing for the humorous suplement El Otorongo, that is published on Fridays for the daily newpaper Perú 21.