Macroevolution - the formation of a new species in one generation is extremely rare in animals, but more common in plants. The way it can happen is through duplication of the entire genome. Organisms which have multiple genome copies are called 'polyploid'. In some plants it's possible to trace back exactly where and when these things happen. For example, a new species of marsh grass appeared in a certain area of marsh in Britain in around 1870. This would have been one faulty cell division resulting in a new species.
Animals are much more complex in structure than plants and rarely reproduce asexually so this kind of thing is much rarer, but it does happen - the plains viscacha rat in Argentina is one example. What must have happened is a faulty cell division leading to a polyploid female and then inter-breeding in her offspring.