It's a symbol, a hybrid creature that represents rebellion and hope. It's not a real animal with real dietary needs.
However, in the context of the story, the Mockingjay symbol is often associated with the same food as the people of Panem:
* Grains: Bread, porridge, etc.
* Vegetables: Roots, fruits, etc.
* Meat: Rarely available, especially during the Hunger Games.
The Mockingjay's food is a metaphor for the struggles and limitations faced by the people of Panem, emphasizing the lack of resources and the constant threat of starvation.