@EmilyJensen1 ...
When you use the Course Import Tool in Canvas to copy content from one course to another (no matter if the course is in the same term/semester or in a different term/semester), your enrollments and submissions should never copy over. Those all remain in the original course. It wouldn't make sense to have student submissions from one course appear in another course because there are (most likely) an entirely different set of students in the new course vs. the past course.
Are you using this Guide to import (copy) content from one course to another?
How do I copy content from another Canvas course using the Course Import tool?
Please let us know the steps you are taking...thanks!