How to display rounded corners to the DataGrid in WPF?

It seems that the DataGrid's horizontal ScrollBar does not work well with the OpacityMask when the window is resized.

You may simply disable it:

<DataGrid x:Name="dgRound" ...
          ScrollViewer.HorizontalScrollBarVisibility="Disabled">

In order to avoid confusion with the nested Borders (e.g. why the inner one has no child element), you may as well use a Rectangle:

<Rectangle x:Name="BDRounded" RadiusX="15" RadiusY="15" Fill="White"/>

A completely different way to create rounded corners on an arbitrary UI element is to set its Clip property to a RectangleGeometry with appropriate RadiusX and RadiusY value.

This could be done by an attached property which could be applied to any FrameworkElement or instances of derived classes. Its code would look like this:

public static class ClipHelper
{
    public static readonly DependencyProperty CornerRadiusProperty =
        DependencyProperty.RegisterAttached(
            "CornerRadius", typeof(double), typeof(ClipHelper),
            new PropertyMetadata(double.NaN, CornerRadiusChanged));

    public static double GetCornerRadius(FrameworkElement element)
    {
        return (double)element.GetValue(CornerRadiusProperty);
    }

    public static void SetCornerRadius(FrameworkElement element, double value)
    {
        element.SetValue(CornerRadiusProperty, value);
    }

    private static void CornerRadiusChanged(
        DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        var element = (FrameworkElement)d;

        if (!double.IsNaN((double)e.OldValue))
        {
            element.SizeChanged -= OnSizeChanged;
        }

        if (!double.IsNaN((double)e.NewValue))
        {
            element.SizeChanged += OnSizeChanged;
            SetClipGeometry(element);
        }
        else
        {
            element.ClearValue(UIElement.ClipProperty);
        }
    }

    private static void OnSizeChanged(object sender, SizeChangedEventArgs e)
    {
        SetClipGeometry((FrameworkElement)sender);
    }

    private static void SetClipGeometry(FrameworkElement element)
    {
        var radius = GetCornerRadius(element);

        element.Clip = new RectangleGeometry(
            new Rect(element.RenderSize), radius, radius);
    }
}

It would be applied like shown below, where the XAML namespace prefix local: might be adjusted to whatever namespace you put the ClipHelper class into. You would also not need to disable the horizontal ScrollBar.

<Grid local:ClipHelper.CornerRadius="15">
    <DataGrid x:Name="dgRound" ...>
        ...
    </DataGrid>
</Grid>