What were the creatures in Hunger Games made of?

The Capital was adept at genetic engineering. The result of their genetic experimentation (as described in the first book) were muttations, known as mutts, which we might call mutants. The dog-like creatures were described as having sharp, metallic plates, and contained the eyes of the defeated tributes in the book. They were specifically designed to either kill the tributes or force them to the center of the arena.

The same genetic process was used to make Tracker Jackers and Mockingjays, although Mockingjays started as birds capable of relaying sensitive information heard from the district populations, spying for signs of rebellion.

They are animals genetically altered by the Capitol.

Beginning during the war with the districts, the Capitol genetically modified animals to use as weapons, commonly called “muttations”.

“During the rebellion, the Capitol bred a series of genetically altered animals as weapons. The common term for them was muttations, or sometimes mutts for short. One was a special bird called a jabberjay that had the ability to memorize and repeat whole human conversations.”
_{^{- The Hunger Games (Chapter 3)}}

They are presumably still carbon-based organic life forms, as one of them, the jabberjays, are able to interbreed with mockingbirds, which are certainly carbon-based organic life forms.

“Instead, the jabberjays mated with female mockingbirds, creating a whole new species that could replicate both bird whistles and human melodies.”
_{^{- The Hunger Games (Chapter 3)}}

The Capitol creates these animals in their labs by genetically engineering them.

“More likely they will be one of the Capitol’s muttations, tracker jackers. Like the jabberjays, these killer wasps were spawned in a lab and strategically placed, like land mines, around the districts during the war.”
_{^{- The Hunger Games (Chapter 14)}}

The wolves that are set upon the tributes in the 74th Hunger Games are specifically described as muttations.

“Muttations. No question about it. I’ve never seen these mutts, but they’re no natural-born animals. They resemble huge wolves, but what wolf lands and then balances easily on its hind legs? What wolf waves the rest of the pack forward with its front paw as though it had a wrist?”
_{^{- The Hunger Games (Chapter 25)}}

Therefore these too would have been genetically engineered by the Capitol.

The wolves were only made to look like the tributes.

By the 75th Hunger Games, Katniss realized that the wolves were not actually the dead tributes.

“It wasn’t real, I tell myself. The same way the muttation wolves last year weren’t really the dead tributes. It’s just a sadistic trick of the Gamemakers.”
_{^{- Catching Fire (Chapter 24)}}

Even more conclusively than that, however, the bodies of the dead tributes are sent back to their families to be buried, so the Capitol can’t use the bodies as pieces of the genetically altered animals.

“All of a sudden, I’m overwhelmed by the thought that Peeta may be already lost, bled white, collected, and in the process of being transported back to the Capitol to be cleaned up, redressed, and shipped in a simple wooden box back to District 12. No longer here. Heading home.”
_{^{- The Hunger Games (Chapter 11)}}

Therefore, they cannot be using the bodies to create these creatures since they return them intact.