The most important thing you can do if you know or suspect that a child is being cruel to animals is to talk to them. Do not ignore even minor acts of cruelty to animals by children, and never make light of the abuse. It's important to distinguish between intentional cruelties by children versus behaviour by very young children who have not developed the maturity to understand that animals have feelings. In the latter case, explain to them that the behaviour is wrong and hurtful, show them how to properly handle animals, and reinforce how important it is to be kind to animals. I've come across numerous studies from universities all over the world (University of New Mexico, University of Warwick in England, Oregon State University, Mills College in California) prove that teaching children to respect and protect even the smallest and most seemingly insignificant animals helps them learn many valuable life lessons.
If a child intellectually understands that it is wrong to hurt animals, and intentionally and routinely does it anyway, the cruelty is more likely to be a symptom of a deeper psychological problem, and the situation requires an immediate and serious intervention. It is a widely accepted fact that kids who witness or experience domestic violence or other abuse are most likely to be abusive to animals because they've learnt to express their anger through physical violence on those weaker than them-animals. Psychiatrists, law enforcement officials, and child advocacy organisations have repeatedly documented that kids who are cruel to animals often turn that violence against humans.
As famed Anthropologist Margaret Mead said, "One of the most dangerous things that can happen to a child is to kill or torture an animal and get away with it." It is imperative that a child who is being intentionally cruel to animals receives professional help. It is also crucial that children are taught to have compassion and empathy for animals at an early age. After all, developing empathy toward animals can be a key step toward developing empathy for and rejecting violence against all beings, including humans.