Remove item from combo box once it's been selected

here is your code

//added optional parameter to pass combobox value after successfully record inserted
        private void BindNamemarks(string cmbName = "")
        {
            try
            {
                SqlConnection conn = new SqlConnection(dataconnection);
                SqlCommand cmd = new SqlCommand("uspmarks", conn);
                cmd.CommandType = CommandType.StoredProcedure;
                conn.Open();
                SqlDataAdapter da = new SqlDataAdapter(cmd);
                DataSet ds = new DataSet();
                da.Fill(ds, "marks");

                NameComboBox.SelectedValuePath = ds.Tables[0].Columns["Id"].ToString();
                NameComboBox.DisplayMemberPath = ds.Tables[0].Columns["Name"].ToString();

                NameComboBox.ItemsSource = ds.Tables[0].DefaultView;
                //if record successfully inserted then remove from the
                if (!string.IsNullOrEmpty(cmbName))
                    NameComboBox.Items.Remove(cmbName);
                conn.Close();

            }
            catch (Exception ex)
            {
                MessageBox.Show(ex.ToString());

            }
        }

        private void InsertButton_Click(object sender, RoutedEventArgs e)
        {
            try
            {

                {
                    SqlConnection conn = new SqlConnection(dataconnection);
                    conn.Open();
                    SqlCommand cmd = new SqlCommand("USPInsertion", conn);
                    cmd.Connection = conn;
                    cmd.CommandType = CommandType.StoredProcedure;
                    cmd.Parameters.AddWithValue("@Name", NameComboBox.Text);
                    cmd.ExecuteNonQuery();

                    MessageBox.Show("Data Saved Successfully", "Message", MessageBoxButton.OK, MessageBoxImage.Information);
                    //call you method to bind combox again
                    BindNamemarks(NameComboBox.Text);

                    conn.Close();
                }
            }
            catch (Exception ex)
            {
                MessageBox.Show(ex.Message.ToString());
            }
        }

After successfully insert to the database return the value  and onload event write the code

comboBox1.Items.Remove(comboBox1.selectedItem)

Note:will only remove from the combobox, not from the datasource binded to the combobox. You may remove it from the datasource and re bind the source if you are using datasource to bind comboBox