I know that is what Stalin did. I never looked at Mao. The new dictator doesn't want anyone around who might challenge them.
Stalin was one of the cadre who followed Lenin. When Lenin died, it wasn't fully clear who was going to follow him. Stalin had been maneuvering behind the scenes for a long time, building his power, and finally emerged as top dog in the late 1920s. That's when people started dying.
Mao was different. He created the Chinese Communist Party, so he was always in charge. He didn't have to clean out a lot of other people who also had potential to claim the throne.