This is something I found frustrating in Silverlight. The problem I ran into is that the instructions I found in the Expression Blend User Guide don't work.

The good news is it is fairly straight forward to add a clipping region by editing the XAML directly in Visual Studio. I prefer editing the XAML in Visual Studio because IntelliSense works, making life much easier. To add clipping to a canvas use the following code:

<Canvas x:Name="Bio" Canvas.Left="435" Canvas.Top="133" Width="400" Height="300">
  <Canvas.Clip>
    <RectangleGeometry Rect="0, 0, 400, 300"/>
  </Canvas.Clip>

  <TextBlock Width="384" Height="54" Canvas.Left="16" Canvas.Top="8" Text="Session Title" x:Name="txtBio"/>
</Canvas>

This will allow you to assign any amount of text in the textblock and it will not spill past the edges of the canvas container.

As you have probably already guessed you can apply this clipping code to almost any object including rectangles and textblocks. In fact you could have shortened the above XAML by applying the clipping region to the textblock itself like so:

<TextBlock Width="384" Height="54" Canvas.Left="16" Canvas.Top="8" Text="Session Title" x:Name="txtBio">
  <TextBlock.Clip>
    <RectangleGeometry Rect="0, 0, 400, 300"/>
  </TextBlock.Clip>
</TextBlock>

Also if you look at the options in intellisense you can create clipping regions based on rectangle, ellipse, line, and path geometries. For now the rectangle seems to be enough for 99% of what I would want to do.