The alarming news comes a matter of days after David posted a video playing around with the pup on Instagram.
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Fans swiftly blasted the father-of-two - who also parents daughter Maryssa from a previous relationship - on the post with one user bluntly demanding: "Why aren't you in prison yet?"
Others expressed deep distress and sadness about the loss of the animal, with one woman saying: "I'm so sad for this poor, defenseless dog."
"You should not be allowed to own any animals ever again. Use some common sense instead of going into a pure rage," a disgusted follower wrote.
One user questioned why David hadn't found a new home for Nugget and said she hopes "Jenelle keeps herself and the kids away" from such a toxic environment.
Jenelle has yet to comment on the situation.