A Chinese professor who posted critical remarks about Mao Zedong on social media is the latest to find out that, under President Xi Jinping, taking issue with the Communist Party’s past brings trouble.

Shandong Jianzhu University last week fired Deng Xiangchao, a professor in the school’s art institute, for his “erroneous remarks” on the Weibo social-media service. In the aftermath of the postings, he was vilified by protesters and online, with some calling him “the People’s Public Enemy.”

Mr. Deng’s posts last month hit at a part of Mao’s legacy that has been tricky for the Communist Party to address: the deaths associated with the revolutionary leader’s policies and campaigns. “If he’d died in 1945, China would have seen 6 million fewer killed in war. If he’d died in 1958, 30 million fewer would’ve starved to death,” said one post. “It wasn’t until 1976 when he finally died that we at last had food to eat. The only correct thing he did was to die.”