To reproduce:
            DataTable table = new DataTable();
            table.Columns.Add("Value", typeof(double));
            table.Columns.Add("Name", typeof(string));
            table.Rows.Add(1, "John");
            table.Rows.Add(3, "Adam");
            table.Rows.Add(5, "Peter");
            table.Rows.Add(12, "Sam");
            table.Rows.Add(6, "Paul");

            BarSeries lineSeria = new BarSeries();
            radChartView1.Series.Add(lineSeria);
            lineSeria.ValueMember = "Value";
            lineSeria.CategoryMember = "Name";

            this.radChartView1.DataSource = table;

        private void radButton1_Click(object sender, EventArgs e)
        { 
            this.radChartView1.DataSource = null; 
        }

The chart data will be still visible. It is necessary to set explicitly the DataSource of the series:
this.radChartView1.Series[0].DataSource = null;