There is no exact date when Martin Luther broke away from the Catholic Church. Although the date October 31, 1517 has often been cited since it’s the day he published the 95 Theses, at that time he still considered himself a Catholic and agreed with most of the Church’s teaches. If he just published the Theses and left it at that, no one would ever have heard of him. The schism occurred over many years as Luther became more and more opposed to Catholicism. Here is a good (but pretty anti-Protestant) video explaining it:
Yes, I know and understand that the makers of this video are not in good standing with the Church, and that their form of so-called Traditional Catholicism is itself schismatic. This video, though, says nothing contrary to the teaching of the Church; it just says things in an excessively negative manner. PLEASE do not make ad hominem arguments.