You can access storyboards from code-behind by giving it a name and referencing that name to use the Begin
method.
<Canvas MouseLeftButtonDown="Handle_MouseDown"
Background="Gray" Width="600" Height="500">
<Canvas.Resources>
<Storyboard x:Name="myStoryboard">
<PointAnimation
x:Name="myPointAnimation"
Storyboard.TargetProperty="Center"
Storyboard.TargetName="MyAnimatedEllipseGeometry"
Duration="0:0:2"/>
</Storyboard>
</Canvas.Resources>
<Path Fill="Blue">
<Path.Data>
<EllipseGeometry x:Name="MyAnimatedEllipseGeometry"
Center="200,100" RadiusX="15" RadiusY="15" />
</Path.Data>
</Path>
</Canvas>
Code-behind:
private void Handle_MouseDown(object sender, MouseButtonEventArgs e)
{
// Retrieve current mouse coordinates.
double newX = e.GetPosition(null).X;
double newY = e.GetPosition(null).Y;
Point myPoint = new Point();
myPoint.X = newX;
myPoint.Y = newY;
myPointAnimation.To = myPoint;
myStoryboard.Begin();
}