Zohran Mamdani, the Democratic front-runner for mayor of New York City, sought to play it safe in the final debate of the race, avoiding contentious issues and pledging to keep the police commissioner. Andrew M. Cuomo, who is running as an independent, and Curtis Sliwa, the Republican candidate, repeatedly attacked Mr. Mamdani and accused him of being inexperienced and evasive. The candidates had tense arguments over how to build housing, combat antisemitism, stand up to President Trump and navigate immigration raids.