Because "Cat Manual" contains many spells that need to be cast through the eyes, previously she couldn't see and could only choose to attack with force. Now that she has sight, she directly uses Spiritual Control to drown this scum. A person like this, keeping him around would only make him a traitor, so his death solves all problems, trash.
She used Spiritual Control to make him walk into the river and sink, only retracting her spiritual power after seeing him swept away by the water.
This person, even if not dead, would be battered senseless by the rapids, especially since he wasn't fully conscious.
She didn't directly kill him; on one hand, she didn't want to stain her hands with blood, and on the other hand, it was also repaying him for dragging her ashore.
