It may come as a surprise, but it seems as though Mao Zedong never ordered the killing of a senior colleague during the Cultural Revolution. Instead of this, he left his former comrades to the mercy of other forces, such as the Red Guards.

These two were not assassinated, but they certainly were punished for their views and removed from desirable positions. For example, Deng Xiaoping was exhiled to Jiangxi province for almost four years, from October 1969 to spring of 1973. There he and his wife were sentenced to physical labor and reeducation in Mao Zedong Thought. Mao did not consider them enemies after Deng completed his self-criticism, but did feel they needed to be reeducated. Actually, this sentence came as a relief to Deng. He had been under considerable stress for the previous three years as he was under political attack during that period. However, after denouncing Deng since 1966, Mao reversed course and wanted to eventually get Deng back into the fold. By 1972, he explained that Deng was different from Liu because Deng had been the leader of the "Mao faction" in the 1930s, had never surrendered to the enemy, had proven himself in battle, and he had done well after the revolution (this personal view was based on his own factually inaccurate rendering of Liu's career, but...). Deng's career was resurrected in 1973.

Liu Shaoqi, though not directly assassinated, effectively did die at the hands of Mao. In 1966, he was replaced by Lin Biao as Party Deputy Chairman, by 1967 was censured, and he and his wife were eventually placed under house arrest. In 1968 at the CCP's Twelfth Plenum, the decision was made to expel Liu from the party. In 1969, he died after medical neglect during his confinement.

The Cultural Revolution occurred for several reasons, but I want to point out the domestic politics of China prior to the revolution. In the last year of the Great Leap Forward-produced famine, 1961, Mao presided over a set of policies to rejuvinate the economy. He still refused to back down on collectivism and much outside criticism. This was a change in attitude. From 1945 until 1965, leadership of the party was essentially the same. Until the mid-1950s, Mao actually was tolerant of debate in the Politburo, and even accepted defeat on certain issues, such as economic policy. However, he changed and pushed aside cautious plans and implemented the GLF. In 1962 he disrupted the recovery of the country with his ideas of class struggle. Liu Shaoqi's view of socialism and coommunism was fundamentally different from Mao's, and he had risen through the party ranks completely differently than Mao had. The two worked together, but were cut from a different cloth. Liu had his own base of strong support, which was something that Mao may have been wary of. Liu and Deng were openly critical of the GLF in reports they drafted on its effects. While they prefaced their remarks with praise for Mao and his vision, they pointed out that statistically the GLF was actually the opposite of “forward”. Liu said that the country was in a dire situation, and he and Deng drafted up some new policies to implement to save the country. Liu, Deng, and Zhou Enlai went to Wuhan, where Mao had retired to, in order to present these new plans and assessments. Mao objected, but Liu and Deng went ahead with them anyways. Mao sensed that the party may be shifting against him, and he pushed back against these (successful) policies. Mao called Liu back in order to chastise him, but Liu was defiant to an incredible level. He effectively said that history would remember their roles in the deaths of millions of people. From this point forward, Liu and Mao were very much at odds with the direction the country should take. During the time leading up to the Cultural Revolution, Mao was not really the most popular person in the party at the time. He had significant opposition. I think that, in part, the CR was Mao's response to what he felt was the party turning away from him and his way of thinking. Liu and Deng were definitely the most vocal critics within the party, but he had critics outside of the party as well. The CR effectively shook up the party leadership from top to bottom (as well as destroying an extremely large amount of traditional Chinese culture, but that's a different story), and Mao was able to gain back control of the country in a stronger manner.

Sources:

China Under Mao: A Revolution Derailed by Andrew G. Walder

Deng Xiaoping and the Transformation of China by Ezra F. Vogel

Mao's Last Revolution by Roderick MacFarquhar and Michael Schoenhals