As per Vedic sciences, Hindu philosophy believes in rebirth unless your Sanchit and Prarabdha Karmas are totally exhausted. 

It also believes in liberation in which once your past karma’s debt is over, you do not take a rebirth.

On the other hand, Garuda Purana says that you can take a birth in animal species which means you can be born like a donkey or a dog. Vedic science on the other hand says that once you get a human body, you will either be liberated or get another human body only.

The message of Garuda Purana can be read and interpreted in a different perspective. In mythology humans are linked to animal tendencies. For example, bull is linked to sexual and non-sexual desires, peacock to vanity etc. Probably, people who wrote Garuda Purana meant that if you do not live according to the Shastras, you may be born as another human body but with animal tendencies and behavior. 

(Disclaimer: The views expressed in this write up are my own).