Cruz's parents were both singers who sang together. Her mother taught her to play the saxophone and piano as well as how to dance and sculpt. Her father was a self-taught guitarist.
She went to Catalonia College of Music in Barcelona, where she received classical training studying the piano and saxophone and receiving a degree in vocal jazz. While she was at Catalonia College of Music, she and three other women founded a flamenco group called Las Migas. They combined their different musical approaches to create a new type of flamenco. It was not long after this that she became well known in the Spanish music scene.
Cruz says that a song must have a story. She believes that her view of songs as stories comes from her mother who was a singer and storyteller. Her mother, she said, also viewed songs as stories.
In 2012, Cruz released her album 11 de Novembre with Raul Fernandez Miró. She met Miró in 2006 and they toured together in Mexico, Argentina, and Brazil. Miró was both guitarist and producer for the album. Their songs have been described as a blend of music genres including Fado, jazz improvisation, and flamenco. Cruz won a Goya Award, Spain's most prestigious film award, for best original song "No Te Puedo Encontrar" in the film Blancanieves. The album received a Gold Award disc.
Granada In 2014, Cruz released her second album Granada, again collaborating with Fernandez Miró. It reflects Cruz's practice of singing in multiple languages: French, German, English, and four Iberian languages. Included on the album is the song "El Cant Dells Ocells," a Catalan folk song previously made famous by Pablo Casals. Another song is "Gallo Rojo, Gallo Negro", a well-known song from the Spanish Civil War. Cruz first understood the story in the song when she was part of a concert honoring the remaining veterans of the International Brigades who fought against Spanish dictator Francisco Franco. Cruz said that she saw tears in the veterans' eyes when they sang the song in their own language. She said, "These people have lived through so much. It's good that I can sing and help them remember." This example illustrates how Cruz comes to understand the stories in the songs she sings.