What happens if I make my minor my major and don't get an undergraduate degree in SPA? Does that mean I can't go to graduate school to become an SLP?

No, people from many different fields, who have worked for some to many years, decide to apply to graduate school to become an SLP. These people still have to apply and get accepted into grad school, but they are considered Post Baccalaureate students. This means that the students will need to take some undergraduate courses from SPA, depending on the prerequisite coursework already completed.