To delete a Dynamic group, you would go to Reporting > Data Digger and then click on the Manage Dynamic Groups tab at the bottom of the page on the left side.
Find the group you want to delete and click on the Edit button on the far right (in the example below, a duplicate Dynamic Group of Boys was created, so one needs to be deleted).
This will take you to a new page where you will see the group in a table. At the bottom of the table there will be a Delete option. Click on this, there will be a pop-up asking if you are sure, and once you click Yes the group will be deleted.
If you wish to delete a Static Group you would follow a similar process. Just click on Manage Static Groups, then Edit next to the group name, where you will find a Delete option.
Find more information here:
Using the Data Digger to create a Dynamic Group or Static Group