Can you replace the border with a Grid and give it a Rectangle that fills the whole area?
<Rectangle Stretch="Fill" RadiusX="10" RadiusY="10" StrokeDashArray="10, 2" Stroke="Black" Fill="White" />
The StrokeDashArray can be used to draw it dotted but a Border has no such property.
EDIT:
Since I noticed you are only dotting the bottom border you could do something like this
<Border Width="100" Height="100" Background="Blue" BorderThickness="0,0,0,1">
<Border.BorderBrush>
<LinearGradientBrush StartPoint="0,0" EndPoint=".2,0" SpreadMethod="Repeat" >
<GradientStopCollection>
<GradientStop Color="Transparent" Offset="0" />
<GradientStop Color="Transparent" Offset="0.3" />
<GradientStop Color="Red" Offset="0.3" />
<GradientStop Color="Red" Offset="0.6" />
<GradientStop Color="Transparent" Offset="0.6" />
<GradientStop Color="Transparent" Offset="1" />
</GradientStopCollection>
</LinearGradientBrush>
</Border.BorderBrush>
</Border>
Adjust the Offset
of the middle two GradientStop's to adjust the width of the red dot/dash. You may also need to adjust the endpoint to make it repeat at your desired interval.