I am not sure how it works for you.
The UserControl's Height is define as 30 but the Rectangle's Height is 200. You already messed the Rectangle in the UserControl. Follow this:
1. Set the Height of the UserControl as "Auto" in UserControl.xaml
2. Remove the Height of the Rectangle.
2. Remove the Margin of the Rectangle as Set it as "8,8,8,8"
<UserControl
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
mc:Ignorable="d"
x:Class="clippingIsue1.UserControl1"
x:Name="UserControl" Width="371.5" Height="Auto">
<Grid x:Name="LayoutRoot" Background="#FF9D0404">
<Rectangle x:Name="rt" Fill="#FF5A5AD2" Stroke="Black" Margin="8,8,8,8"/>
</Grid>
</UserControl>