Mendieta was born on November 18, 1948, in Havana, Cuba, to a wealthy family prominent in the country's politics and society. Her father, Ignacio Alberto Mendieta de Lizáur, was an attorney and the nephew of Carlos Mendieta, who was installed as president by Fulgencio Batista for just under two years. Her mother, Raquel Oti de Rojas, was a chemist, a researcher, and the granddaughter of Carlos Maria de Rojas, a sugar mill owner celebrated for his role in the war against Spain for Cuban independence. Ana, aged 12, and her 15-year-old sister Raquelin were sent to the United States by their parents to live in Dubuque, Iowa through Operation Peter Pan, a collaborative program run by the US government and the Catholic Charities. Ana and Raquelin were among 14,000 children who immigrated to the United States through this program in 1961. Mendieta's first two years in the United States consisted of constant alternation between foster homes and orphanages. The sisters were able to stay together during this time due to a power of attorney signed by their parents, which mandated that they not be separated. The two sisters spent their first weeks in refugee camps, and then moved between several institutions and foster homes throughout Iowa. In 1966, Mendieta was reunited with her mother and younger brother. Her father joined them in 1979, having spent 18 years in a political prison in Cuba for his involvement in the Bay of Pigs invasion.