She was born Alexina Sattler in Cincinnati, Ohio in 1906. The youngest daughter of prominent surgeon Robert Sattler, Alexina was nicknamed "Teeny" by her mother Agnes Mitchell because of her low birth weight.
Sattler at first thought of becoming an artist and went to Paris in 1921, where for a time she studied sculpture with Constantin Brâncu?i at the Académie de la Grande Chaumière in Paris. She first met Marcel Duchamp in 1923 at a ball given in her honor by American sculptor Mariette Benedict Mills, the mother of a close friend. In 1929 Teeny married Pierre Matisse, an art dealer and the youngest son of Fauve artist Henri Matisse. They had three children: Jacqueline, Paul, and Peter. Throughout 1938, Henri Matisse made a series of portrait sketches of Alexina. When her husband was mobilized in Paris at the outbreak of World War II, she ran his gallery for some months. In 1949 Pierre and Teeny separated due to Pierre's infidelity with Patricia Kane Matta. She received in the subsequent divorce settlement many important paintings.
In the autumn of 1951 she was invited by Dorothea Tanning to go on a weekend trip in Hunterdon County. It was on that trip that she once again met Duchamp, and romance developed shortly thereafter. They were both avid chess players. Teeny and Duchamp married in New York City on January 16, 1954. They lived in New York and in Paris; around 1958, the couple began spending summers in Cadaqués, Spain, on the Costa Brava. They were together until his death in 1968. Following Duchamp's death, Alexina moved to Villiers-sous-Grez, near Paris, where she assembled an archive of photographs and other material documenting the life and work of her late husband. She maintained a close friendship with many of Duchamp's friends, including Jasper Johns, Richard Hamilton, composer John Cage, Gianfranco Baruchello, and choreographer Merce Cunningham.Alexander Calder presented her with individually designed jewelry. She also served as an honorary trustee of the Philadelphia Museum of Art, which has the largest collection of Duchamp's work.