On March 5th 1953, Stalin died and Mao publicly mourned his death and called him "The greatest genius of our time", respecting him and his Marxist ideals. However, with his death, the future leadership of the Soviet Union and of world communism became very uncertain. While Stalin was alive, he had contributed to the rise of the communist party in China and had helped China with industrialization and their economy. And during this time, while Mao and Stalin's relationship was not perfect, Mao and Stalin's Marxist ideology were similar and kept the two countries allied. But now, with Stalin's death, the USSR would have a new leader, Nikita Khrushchev, who would differ greatly from the leader before him.
Nikita Khrushchev came to power in 1953 after Stalin's death, but in February, 1956, during the 20th Congress of the Communist Part of the Soviet Union, Khrushchev gave his 'Secret Speech', On the Cult of Personality and Its Consequences. This speech shocked and transformed the communist world both within the Soviet Union and in places outside like China. Khrushchev attacked Stalin's personality cult and the repression and tyranny that came from it. He criticized the purges and the excessive centralization of power, and overall, this speech brought fourth the policy of De-Stalinization throughout the soviet Union which tried to change and override many of Stalin's policies.
The reaction by Mao in China was mixed. On one hand, Mao had been modeling much of his reign on how Stalin had reigned including creating his own 'Cult of Personality', so he was quite concerned about this. On the other hand, Mao saw this as an opportunity to assert himself more into the light as a global leader of communism.
The most impactful policy change that came from this 'secret meeting' in regards to international policy with the world was coined 'Peaceful Coexistence'. This was the approach Khrushchev wished to take to handle the struggle between the socialist block and the capitalist one. His idea was that direct military conflict was not inevitable between socialism and capitalism, but that instead the two could compete peacefully through things like economic development and political influence, and avoid a nuclear war.
This greatly differed from Mao's idea of 'Preventive War' and was the first major split in ideology between the two countries that led to much future conflict. Mao's policy was the idea that revolutionary struggle should be waged against imperial, capitalist forces in order to advacnce the socialist cause even if that means another world war. He believed that trying to confront imperialism through peaceful means would not work and instead allow the imperialist nations to take over and dominate the world. Mao was influenced by his experience in the Korean War where he did confront imperial armies to further socialism. Mao went as far as to supposedly say, "If we lose 300 million people, that would not matter. The important thing is that we win the revolution." China went on to publicly refer to the USSR as "revisionist" in 60s and complained how the USSR had tried to reach agreements with the "imperialists" and abandon the revolutionary struggle. He accused the USSR as disarming the revolution through the policy of peaceful co-existence and for going against Marxist-Leninist principles. This massive ideological conflict really started to create huge amounts of distrust and animosity between the two countries and would ultimately lead to more and more problems.
Because of these clashing ideas about how socialism should interact with the world, Mao believed China and himself had the new role to play as the leader and center of the global communist movement since Khrushchev was too cautious. Khrushchev and the USSR obviously did not agree with this and gave no power or right to China. Historian and author Ronald C. Keith summarized this exchange and put very well, "Of course, no great power would have ceded leadership of its domain to an ally that was militarily less powerful, economically weaker, and run by a radical megalomaniac." The split over ideology continued to grow and began to boil over to national interests being in play as seen nect.
As the ideological differences compounded, the USSR mistrust towards China grew and the willingness to help China diminished greatly. Two of the clearest examples of this is the decrease of economic aid in the late 50s leading up to the withdrawal of all aid and technology in 1960. The second being the cancellation of the 1957 nuclear assistance agreement between China and the USSR in 1959.
Going back to the first one, remember from earlier that 7% of China's economy was aid from Russia, but in the late 50s, an article by William Hayter put it that "Six neutral countries whose total population is less than that of China, have between them had five times as much from Russia as China got", and this is before the public split of the two countries in 1960 that ended all aid to China.
Now in regards to the nuclear assistance agreement being cancelled, this clearly shows how the USSR no longer trusts Mao and China. This agreement was the USSR sending supplies, technology and Soviet experts to China to help them develop their first nuclear bomb, but as the ideological split grew and grew with the disagreements about the future of the socialist world and revolution, the USSR cut off this program and withdrew everything that could help China develop a bomb.
Both of these events go to show how much the ideological split and mistrust that grew from it between these two countries had gone to impact economic and national issues. Edward Crankshaw in his article 'K v Mao' talks about a summary of a note from Khrushchev to Mao , 1964 that puts in perfectly, "Ideological differences between our two parties have now been carried over to affect relations between our two countries and to shake the foundations of our friendship".