Try
For Each row As DataGridViewRow In DataGridView1.SelectedRows
ds.Tables(0).Rows(row.index).Delete()
Next
da.Update(ds, "Part")
DataGridView1.Refresh
MessageBox.Show("Success!")
By the way, your line:
DataGridView1.Rows.Remove(DataGridView1.SelectedRows(0))
is obsolete, since you've got a bounded datagridview, a refresh will suffice.