In Of Mice and Men, Carlson is not as outwardly violent or as insecure as Curley, but they both essentially behave according to their own self-interests.
There is no indication that Carlson adheres to some religious doctrine or that he has a significant relationship with God, so we can eliminate Divine Command Theory because this theory states that one acts out in accordance with God's law.
Carlson is too thoughtless to be considered an Ethical Formalist. An Ethical Formalist is someone who makes decisions based on their logical content. You could argue that Carlson bases his behavior on a universal law of selfishness or even a Darwinian "survival of the fittest." However, there is no evidence that he considers his actions with respect to logical arguments.
Utilitarianism states that one must act in order to achieve the greatest overall happiness. Therefore, one must consider the consequences of any action in order to determine if it is the right course of action. Carlson personally practices this as he acts in order to obtain the greatest happiness for himself. But he certainly is not a social utilitarian, meaning he does not consider the "overall" happiness of others in addition to himself. Not to mention, there is no evidence that he considers all the consequences of his actions.
For example, he may be correct that killing Candy's dog is the humane thing to do, certainly if the dog is suffering. But he does so out of selfishness. He is annoyed with the dog's smell. He uses the "put him out of his misery" argument to justify killing the dog. His real motivation is to be rid of the inconvenience of having to live the dog. And because Carlson is relatively dispassionate about the dog and Lennie's death, it is likely that he does not take all consequences into consideration (including if and how others might perceive his actions and words and if they might react aggressively towards him.)
Carlson is an egoist. He does what he thinks is in his own best interest. This doesn't mean he necessarily wants to harm others. It just means that he puts his own interests first. Still, it is hard not to call him a thoughtless opportunist. When George and Slim are distraught with Lennie's death, Carlson says, "Now what the hell ya suppose is eatin' them two guys?" Either he is oblivious to their grief or he just doesn't care. In either case, Carlson just doesn't stop to consider why they might be distraught.