1) Use animations for your fade out and slide up. For fade, you'll be doing a DoubleAnimation on the Opacity property. For sliding items up, you'll be doing an animiation on the TranslateTransform property. See these MSDN guides: http://msdn.microsoft.com/en-us/library/windowsphone/develop/jj206955(v=vs.105).aspx and http://msdn.microsoft.com/en-us/library/windowsphone/develop/system.windows.media.translatetransform(v=vs.105).aspx
2) For actually properly moving things up, you'll want to capture the Completed event from the animiation (http://msdn.microsoft.com/en-us/library/windowsphone/develop/system.windows.media.animation.timeline.completed(v=vs.105).aspx). When the animiation completes, remove those controls from the StackPanel inside the ScrollViewer, and undo any position animation you did on the items below it to animate them 'sliding' up.
3) After creating an animiation, you need to add it to a storyboard:
Storyboard sb = new Storyboard();
sb.Children.Add(fadeGrid);
Storyboard.SetTarget(fadeGrid, myRectangle);
Storyboard.SetTargetProperty(fadeGrid, new PropertyPath("(UIElement.Opacity)"));
sb.Begin();
The syntax for the propertypath but not be quite perfect, but you get the idea. You can see another example that specifically mentions opacity here: http://blogs.msdn.com/b/silverlight_sdk/archive/2008/03/21/silverlight-animations-a-walkthrough.aspx