Mata was born in Mexico City. He studied guitar privately for three years before enrolling in the National Conservatory of Music. From 1960 to 1963 he studied composition under Carlos Chávez. In 1964 he received a Koussevitzky Fellowship to study at Tanglewood. There, he studied conducting with Max Rudolf and Erich Leinsdorf and composition with Gunther Schuller.
He composed several works in the 1950s and 1960s, including three symphonies, chamber works, sonatas, and works for ballet. His third symphony and some of his chamber works have been recorded.
In 1965 he was appointed head of the Music Department of the Universidad de México and conductor of the Guadalajara Orchestra. He also conducted the orchestra at the University, which later became the Universidad Nacional Autónoma de México (UNAM) Symphony Orchestra. In 1972, he left Mexico to take the position of principal conductor of the Phoenix Symphony Orchestra.
From 1977 to 1993 he was music director of the Dallas Symphony Orchestra and guest conductor of several famous orchestras in the U.S, Europe and Latin America. He recorded over fifty albums, most of them with the UNAM Symphony Orchestra, the Dallas Symphony Orchestra and the London Symphony Orchestra.
On the morning of January 4, 1995, Mata and a passenger were en route from Cuernavaca, Mexico to Dallas, Texas. Mata was piloting his own Piper Aerostar. One engine failed shortly after takeoff and the plane crashed during an emergency landing attempt. There were no survivors.