Click on the calendar image near the textbox.
Choose a date then clear it using the second image near the textbox.

<< Thursday, February 09, 2012 >>

Check also the client side clear example.

<ASP:TextBox runat="server" ID="txtDate"></ASP:TextBox>

<obout:Calendar runat="server" ID="Calendar1"
                         DatePickerMode="true"
                         TextBoxId="txtDate">
</obout:Calendar>

<asp:ImageButton Src="images/DeleteBtn.gif" Id="imgClear" runat="server" OnClick="imgClear_Click" />

<script runat="server">
protected void imgClear_Click(object sender, EventArgs e)
{
    Calendar1.SelectedDate = new DateTime(0);
}
</script>