In the cell, which organelle has the function of using oxygen in the breakdown of glucose, releasing energy and carbon dioxide?

The correct answer will be-mitochondria.

Explanation:

Mitochondria is double-membrane organelle which is associated with the production of energy molecule called ATP.  

This ATP is produced either through respiration or breakdown process of food using oxygen called aerobic respiration or without oxygen called anaerobic respiration.

Since mitochondria are associated with the oxidation of food using oxygen which accepts the electron from the electron transport chain in the end and helps produce ATP therefore, mitochondria is the correct answer.