There are many possible approaches depending on whether responses are collected at the same time and whether students are given access to the responses.

Responses Collected at Different Times

If the activities are run successively, you can clear in between to start a new run. No results are ever deleted. Clear Responses just creates a new run and reports can be created for past runs.

Open the activity before the next group is given access, and click Clear Responses at the bottom of the screen. More details at How to Clear Responses.

Students Never See Responses

No special action is needed in this case. For example, if you use an asynchronous response link, students submit responses but never see responses submitted by other participants. All the responses across classes or groups will be in the report together. Then when you sync to your Blackboard grade center, only students on the roster for the selected class are synced to the corresponding grade center. Student responses for students not in the course are ignored.

Responses Collected at Same Time and Students See Them

If the activities are run concurrently and students do see responses, then the only work around is to create duplicates of the activities. To duplicate, from your Activities screen, check the activity you want to duplicate. Then select Duplicate in the menu that comes up. More details at Move and Duplicate Activities. Consider editing the activity title to  include group information, such as section number, so you can easily tell them apart.