Using this
answer from StackOverflow[
^] with some datatriggers should do the job.
<Window x:Class="MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="MainWindow" Height="350" Width="525">
<Grid>
<DatePicker Height="30" HorizontalAlignment="Left" Margin="73,48,0,0" Name="DatePicker1" VerticalAlignment="Top" Width="299" />
<RadioButton Content="Year" Height="16" HorizontalAlignment="Left" Margin="90,122,0,0" Name="rbYear" VerticalAlignment="Top" />
<RadioButton Content="Month" Height="16" HorizontalAlignment="Left" Margin="88,162,0,0" Name="rbMonth" VerticalAlignment="Top" IsChecked="True" />
<RadioButton Content="Date" Height="16" HorizontalAlignment="Left" IsChecked="False" Margin="90,195,0,0" Name="rbDate" VerticalAlignment="Top" />
</Grid>
<Window.Resources>
<Style TargetType="{x:Type DatePickerTextBox}">
<Style.Triggers>
<DataTrigger Binding="{Binding IsChecked, ElementName=rbYear}" Value="True">
<Setter Property="Control.Template">
<Setter.Value>
<ControlTemplate>
<TextBox x:Name="PART_TextBox" Text="{Binding Path=SelectedDate, StringFormat='yyyy',
RelativeSource={RelativeSource AncestorType={x:Type DatePicker}}}" >
</TextBox>
</ControlTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
<DataTrigger Binding="{Binding IsChecked, ElementName=rbMonth}" Value="True">
<Setter Property="Control.Template">
<Setter.Value>
<ControlTemplate>
<TextBox x:Name="PART_TextBox" Text="{Binding Path=SelectedDate, StringFormat='MMMM',
RelativeSource={RelativeSource AncestorType={x:Type DatePicker}}}" >
</TextBox>
</ControlTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
<DataTrigger Binding="{Binding IsChecked, ElementName=rbDate}" Value="True">
<Setter Property="Control.Template">
<Setter.Value>
<ControlTemplate>
<TextBox x:Name="PART_TextBox" Text="{Binding Path=SelectedDate, StringFormat='dd',
RelativeSource={RelativeSource AncestorType={x:Type DatePicker}}}" >
</TextBox>
</ControlTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
</Style.Triggers>
</Style>
</Window.Resources>
</Window>