Does "speak one's mind" mean "speak in a straightforward way"? Does it have negative nuance?
Yes, that's correct. To "speak one's mind" means to express one's own thoughts or opinions in a straightforward or honest way. It doesn't have a negative connotation, and is mostly thought of as a good thing. Ex: I admire him. He always speaks his mind. Ex: She is true to herself and always speaks her mind.