You can try using
this.gridGroupingControl1.Table.DeleteRecord
Or, you can work directly with your datasource and use methods on it to delete its records.
With the 3010 code base, if you use the new record selection support,
this.gridGroupingControl1.TableOptions.ListBoxSelectionMode = SelectionMode.MultiExtended;
this.gridGroupingControl1.TableOptions.AllowSelection = GridSelectionFlags.None;
then this button handler will delete the selected records.
private void button2_Click(object sender, System.EventArgs e)
{
foreach(SelectedRecord r in this.gridGroupingControl1.Table.SelectedRecords)
this.gridGroupingControl1.Table.DeleteRecord(r.Record);
}