In your code you are just removing the items from the listview, but you are not deleting anything. You must use File.Delete, something like this:
if (listView1.SelectedItems.Count > 0)
{
var confirmation = MessageBox.Show("Do You Really Want to Delete the Item", "Delete", MessageBoxButtons.YesNo, MessageBoxIcon.Question);
if (confirmation == DialogResult.Yes)
{
for (int i = listView1.SelectedItems.Count - 1; i >= 0; i--)
{
ListViewItem itm = listView1.SelectedItems[i];
File.Delete(itm.Text.ToString());
listView1.Items.Remove(itm);
}
}
else
MessageBox.Show("None Selected");
}