I think you and I are in the same boat, I'm working on a Metro card game application and I'm not relly happy with what I've found as far as Drag and Drop goes. My inital approach was going to be to have a grid \ stackpanel or other underlying framework that the user could drag a card image ( acually a custom control ) over and then the image would snap to that framework when the user let go. I have not yet found a suitable way to obtain this behavior however because it seems like drag-drop of controls from one parent to another is not supported in Metro.
As far as your question goes, the sliding effect that you are refering to is most likely intertia, You can disable this by not setting the TranslateInertia mode, for example
Ellipse el = new Ellipse();
el.Fill = new SolidColorBrush(Windows.UI.Colors.Magenta);
el.ManipulationMode = (ManipulationModes.All ^ MainipulationModes.TranslateInteria);
//more code to add your ManipulationDelta handler etc.
You can also gain some control over the Interia by adding a handler for MainipulationInertiaStarting, though just setting e.Handled = true in the handler does not disable interia entirely for me as others have suggested.
I'd love to hear back from you and see what approach you've come up with for snapping cards, at this point I'm considering just using a large Canvas object and writing my own customer handlers for mouse moved to get card objects to be draggable and then snap into a row or other location on the playing board.
Cheers,
James