Díez de Medina came from a wealthy local Criollo upper-class family and increased his wealth through active trade.
He lived in the Palacio Diez de Medina, which is today the National Museum of Art, La Paz.
When the uprising of Túpac Katari against the Spanish colonial rulers was suppressed in 1781, Díez de Medina was the responsible judge who ordered death by quartering.
When the Governor of Chile, José de Santiago Concha Jiménez Lobatón was recalled to Buenos Aires, Tadeo Diez replaced him for a few weeks (from December 1801 to January 1802), until his successor, Luis Muñoz de Guzmán, appointed by King Charles IV, arrived from Lima to take office.
In February 1803, Tadeo Diez became semi-paralyzed and seriously affected by smallpox, so he no longer attended court.