namespace MyCodeNamespace
{
  public class Clip
  {
    public static bool GetToBounds(DependencyObject depObj)
    {
      return (bool)depObj.GetValue(ToBoundsProperty);
    }

    public static void SetToBounds(DependencyObject depObj, bool clipToBounds)
    {
      depObj.SetValue(ToBoundsProperty, clipToBounds);
    }

    public static readonly DependencyProperty ToBoundsProperty =
      DependencyProperty.RegisterAttached("ToBounds", typeof(bool),
      typeof(Clip), new PropertyMetadata(false, OnToBoundsPropertyChanged));

    private static void OnToBoundsPropertyChanged(DependencyObject d,
      DependencyPropertyChangedEventArgs e)
    {
      FrameworkElement fe = d as FrameworkElement;
      if (fe != null)
      {
        ClipToBounds(fe);
        fe.Loaded += new RoutedEventHandler(fe_Loaded);
        fe.SizeChanged += new SizeChangedEventHandler(fe_SizeChanged);
      }
    }

    private static void ClipToBounds(FrameworkElement fe)
    {
      if (GetToBounds(fe))
      {
        fe.Clip = new RectangleGeometry()
        {
          Rect = new Rect(0, 0, fe.ActualWidth, fe.ActualHeight)
        };
      }
      else
      {
        fe.Clip = null;
      }
    }

    static void fe_SizeChanged(object sender, SizeChangedEventArgs e)
    {
      ClipToBounds(sender as FrameworkElement);
    }

    static void fe_Loaded(object sender, RoutedEventArgs e)
    {
      ClipToBounds(sender as FrameworkElement);
    }
  }
}

<Border myNameSpace:Clip.ToBounds="true">
...
</Border>