Dreams involving animals, especially those in distress, can often reflect our feelings of empathy, guilt, or concern for others. In your dream, the sick white cat may represent someone or something in your life that you care about but feel powerless to help.

The act of cutting off the cat's head with a bread knife could symbolize a drastic or extreme solution to a problem you perceive. This might indicate that you are feeling frustrated or overwhelmed by a situation in your waking life, and you may believe that taking extreme measures is necessary to find a resolution, even if those measures don't truly address the underlying issue.

Feeling that you didn't do anything wrong could suggest a level of disconnection from the consequences of your actions or a rationalization of your choices, indicating that you might be struggling to confront the reality of a situation or your feelings about it.

Overall, this dream may be urging you to reflect on how you handle problems and whether the methods you consider are genuinely beneficial. It could be a call to seek more compassionate and constructive solutions rather than resorting to drastic measures. Consider what areas of your life might need your attention and how you can approach them with care and thoughtfulness.