Mayor Bill de Blasio, confronting the gravest crisis of his young administration, has been by turns composed and defiant, empathetic and indignant, urging calm in one moment and lashing out in frustration the next. In other words, he has acted like himself: a confident but mercurial leader whose singular political style has not wavered, even in the face of a potentially career-defining flash point over the police and race. In a sharp turn from his predecessors — the pugnacious, prosecutorial Rudolph W. Giuliani and the business-minded Michael R. Bloomberg — Mr. de Blasio, a political professional who promised a warmer,...