Yes. You have to take all the courses required by both your major and the Data Science Minor. Several classes are in both lists. That is fine. Except that:
CS and CE majors cannot double-count any course as both a Major Elective (aka 500-level elective) and a Data Science minor course. For example, if you take CSCE 587 you can count it towards your Major or towards your minor, but not both.
CIS majors will have to Petition the department for substitution to CSCE 146 in the Data Science minor, and cannot double-count CSCE 520 or their Major Elective course.