Scrollview Scroll внизу
scrollView.fullScroll(View.FOCUS_DOWN)
AndroidGeek
scrollView.fullScroll(View.FOCUS_DOWN)//add to the xaml <ScrollViewer ScrollChanged="scroll_ScrollChanged">
private void scroll_ScrollChanged(object sender, ScrollChangedEventArgs e)
{
ScrollViewer sv = (ScrollViewer)sender;
sv.ScrollToEnd();
}