<ListBox Grid.Row="1" Height="120" HorizontalAlignment="Left" Name="list_proc" VerticalAlignment="Bottom" Width="243" 
                 ItemsSource="{Binding Mode=OneWay, ElementName=procDomainDataSource, Path=Data}" 
                 Margin="12,0,0,0"  DisplayMemberPath="name" />

list_proc.Items.Clear();

list_proc.Clear(); //такого свойства вообще нет

list_proc.ItemsSource = null;