You would need to create another Graphic that clones original Graphic's geometry and copies original Graphic's Attributes.For example, you can subscribe to the source layer's MouseLeftButtonDown
private void GraphicsLayer_MouseLeftButtonDown(object sender, GraphicMouseButtonEventArgs e)
{
var l = MyMap.Layers["DestinationLayer"] as GraphicsLayer;
// This code clones the geometry (i.e. Polygon)
var g = new Graphic() { Geometry = Geometry.Clone(e.Graphic.Geometry) };
// This code clones the attributes.
foreach (var item in g.Attributes)
g.Attributes[item.Key] = item.Value;
l.Graphics.Add(g);
}