Secondly, because his purpose is not here. Xiong Er, bear, is also two lives. Logger Vick's purpose is only to chop wood. So he won't think about anything else, because Logger Vick is a dead brain. His IQ can't support him to think of a fundamental way to achieve the purpose of chopping wood. Otherwise, Xiong Er and Xiong Da could not stop him from cutting down a whole forest.
Finally, it is because of its educational function. The audience of this cartoon is children, so it can't be so violent. Naturally, there can't be a scene of killing Xiong Da Xiong Er, otherwise it will instill wrong values in children.