Only intelligent critters would do it. Animals grab and hold on.
Maybe, maybe not? It depends on how you view 'release'. Release could just be letting go fast enough to get a better kill grip as the prey weakens--because you're going to grab them again and again and again from an increasingly better position each time.
When killing smaller prey, a dog might grab, then shake hard. The prey is disoriented, so they quick-release or even quick-drop to shift grip now that they have access to a more tender body part, grab, shake hard, rinse and repeat. Whatever it is will be dead within a few rounds of this.
"Hey, human, look, look! I brought us breakfast! I am the BEST!!!"
"...haha, just kidding! It's all mine!"
<The squirrel stares at you with silent and accusing black eyes.>