not have the heart to do sth可不是“没心情做某事”，而是“不忍心做某事”。

【例句】
I really don’t have the heart to tell him the truth.
我真的不忍心告诉他真相。

That's why I didn't have the heart to destroy them.
这也是我不忍心摧毁他们的原因。