You cannot set margin to your shadow, so you could "hide" another simple
Border behind your "real" Border.
Wrap them in a Grid that will hold both of them in the same place.
Set your margin on that Border, and set the shadow effect on it as well.
<Grid>
<Border Margin="20,20,0,0">
<Border.Effects>
<DropShadowEffect />
</Border.Effects/>
</Border>
<Border x:Name="YourOriginalBorder"/>
</Grid>