Could this be The Battle Begins, first book of the Unnaturals series by Devon Hughes?
Castor has always been a stray, prowling with his pack in the back alleys of Lion's Head. That is, until the day that he's captured and taken to a dark laboratory full of terrifying creatures. They're called Unnaturals, and they're made to fight.
Soon Castor is transformed from a mutt into a powerful beast with huge eagle wings—and he's thrust into the fighting ring. He knows he'll need all of his courage to survive. But it will take unexpected human and animal allies and something even more than courage for him to save the Unnaturals....
From this review:
Castor and his brother Runt are living with their pack on the ground level of a society where the air and environment has become poisoned enough that the well-to-do live in the sky. Marcus is one of these people, living with his parents and enjoying watching the Mega Monster Mash-up tournaments that have become popular. Even though his older brother, Pete, works as a medic for the animals, he thinks that these are virtual fights, and that the animals are not real. Leesa, however, knows differently-- her chihuahua, Pookie, was stolen and turned into a chihuahua/spider mix who fought in these televised battles. Castor also finds out how real these events are after he is stolen from the streets and experimented on until he becomes a dog/eagle mix and starts to train for the fights. Living alongside creatures like octopus/elephant mixes, Castor has to decide if he will turn into a killer or remain true to himself. With the help of the humans, the animals investigate ways that they might be able to break free for the horror of the games and make it to the elusive Greenplains.
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novel scientist animals mutated "dog * wings"