His family moved to Hidalgo de Parral in the state of Chihuahua, where at age 6 he starts modelling clay, an art his mother practised.
At his return to Mexico, secretary of public education José Vasconcelos invited him to be part of his cultural project, where he makes his first grand format sculptures at the Secretariat's central courtyard.
By 1922 he had the sculpting professorship of the National Institute of Fine Arts, and he was awarded the project for the making of the Monumento a la Patria, at the Pérgolas Garden of the Chapultepec Castle.
His funeral was attended by important characters such as David Alfaro Siqueiros, Rufino Tamayo, Miguel Alemán, Justino Fernández, and Guadalupe Rivera Marín, among others.
All along his career, Asúnsolo showed a style influenced by classical art and his mentors Maillol, Mariano Benlliure, Mateo Inurria, Auguste Rodin, Arnulfo Domínguez Bello, and Enrique Guerra, among others.