He was the firstborn son of Cardinal Pedro González de Mendoza and Mencía de Lemos and a member of the powerful House of Mendoza family. He was schooled by his father and his uncle Diego Hurtado de Mendoza y Quiñones. He was the brother of Diego Hurtado de Mendoza, 1st Count of Melito.
In 1492, Rodrigo married Leonor de le Cerda in a secret wedding. They would go on to live in the Castle of Jadraque which belonged to her family. After her death in 1497, he went to Italy where he became familiar with the architecture of the Italian Renaissance.
As punishment, he was incarcerated until the death of the queen in 1504.
Rodrigo was favored in the dispute by Philip I of Castile and Íñigo by Ferdinand II of Aragon. He played an active political and military role in the quelling of the Revolt of the Brotherhoods.
