@Mitch Willis Thanks for reaching out. Logic app does provide Azure AD connector which you can leverage in your workflow to perform multiple actions listed here.
I do see add user to group and remove member from group that can be leveraged for your requirement. In case it doesn't help then you can always leverage the Native HTTP action to make any HTTP call to the specified URL. In your case you can leverage the Azure AD REST API to perform the operation which connector does not support as of now.