BEIJING—China’s Communist elite is marking the launch of the market reforms that fueled the country’s economic miracle with an unusual amount of discord, much of it directed at President Xi Jinping.

In the weeks leading up to Tuesday’s 40th anniversary celebrations, Mr. Xi’s brand of forward-leaning foreign policy and strongman-led national development has drawn fire. Critics within the party are pointing to China’s flagging economy and down-spiraling relations with the U.S. as proof Mr. Xi has concentrated too much authority...