What would happen if cheetahs were removed from the ecosystem?

This is an interesting question. It is difficult to estimate the effect of the loss of any given species on an ecosystem because of its inherent complexity. Ecosystems are dynamic structures, complete with all sorts of feedback mechanisms, so it is hard to judge the impact of a specific change.
In the case of the cheetah, it is even more difficult to say. For one, cheetahs inhabit a variety of ecosystems, each with unique characteristics. There are various subspecies of cheetah. So the cheetah's disappearance would have differing effects in each case. In general terms, however, the cheetah is a predator and hunter at the top of the food chain, so its disappearance would impact its prey and so on down the line. It is usually the case that the disappearance of animals and organisms that are more widespread in the ecosystem and food chain have the greatest impact.
Sadly, cheetahs are already disappearing. They are vulnerable and even on the verge of being endangered world-wide. Their numbers have dwindled due to a number of factors: poaching, illegal pet trade, habitat loss, etc. They also have unique genetic characteristics and suffer from inbreeding, which has made them vulnerable to disease.