Newt Scamander leaves Hogwarts under a cloud, having been accused of endangering students. Albus Dumbledore, then a teacher at Hogwarts, argued against his expulsion (WFT). Soon after, Newt begins working for the Ministry of Magic (FB).
We don't know the actual year that Scamander was expelled, but it would have been before 1915.
One of the companion books published along with the release of the film states that Newt's close friend Leta Lestrange was responsible for the experiment which went wrong and endangered other students, and that Newt chose to take the blame for it.