I need help writing a character that doesn't like other people and rarely shows emotion due to high amounts of emotional trauma? He would let a person die if they were no longer of any use to him.
Emotionless characters still have emotions. They just don't show it.
If your emotionless character is your POV character, you can still describe all the thoughts and feelings of the character... but emphasize that they don't show it. The Hunger Games does a good job of doing this by either describing how Katniss sees her expressionless face on the screens, others comment how she's so hard to read, or she shows a general distrust of people who exhibit emotions (she thinks they're insincere).
If your emotionless character is not your POV character, follow the example of how CS Lewis describes the Hrossa in Out of the Silent Planet. Dr. Random repeatedly misreads the Huossa or simply has no idea what they are thinking. Even when the Hrossa speak, Ransom can't figure out what they mean because they're so expressionless.