If you have a year-long course and expect minimal movement of students enrolling, dropping or moving between groups then the best course of action may be to manually move students,unenroll dropped students, and have new students add to the group using the group enrollment key.
However, if there will be significant movement of students or if your course is semester-long then archiving the current group and creating a new group for the second semester may be a better solution.
As a general rule I rarely recommend deleting a group entirely since deleting the group will completely remove all record of activity including submitted work, quiz scores, etc. Archiving a group hides the group from your active list of groups and sets the group to read only for students. According the Edmodo help document,
Once a Group is archived, students will not be able to reply or post anything to the Group. Students in an archived Group will still be able to direct message you, but the Group activity is inactive. All Posts and data from the group will be saved, and you can view the Posts and retrieve any previously created quizzes or assignments from your archived Groups. You can also restore an archived group at any time, making it active again.
Here are a few screen shots demonstrating the steps for archiving a group.
