"Killing trees" usually refers to using a lot of paper, which comes from trees.
If someone tells you you are killing "too many trees," it usually means that you are wasting paper.
I see that your quote says "so many trees." To understand the exact message that was being communicated to you, I think it would be important to pay attention to the tone of your manager's voice. It's possible that he or she was paying you a compliment, but also asking you not to use so much paper. It really depends on the tone, so this may not have been his or her meaning.
Teaching ESL to Adults