Its not a good idea to put both stackpanel and scrollviewer in the same grid. As they do not have any ZIndex property, i believe the right panel came on top and the left panel stopped responding to mouse event. try using different columns:
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto"/>
<ColumnDefinition Width="Auto"/>
</Grid.ColumnDefinitions>
<StackPanel Orientation="Vertical" Width="230" Grid.Column="0">
<Label Content="write message"/>
<RichTextBox Height="200" >
<FlowDocument/>
</RichTextBox>
<Label Content="Remaining Characters: 160" />
<TextBox />
<Button Content="SEND"/>
</StackPanel>
<ScrollViewer VerticalScrollBarVisibility="Auto" Grid.Column="1" >
<StackPanel CanVerticallyScroll="True" Margin="10,0,0,40" Orientation="Vertical" MinHeight="800" ScrollViewer.CanContentScroll="True">
<Border Width="200" Height="600" Background="LightBlue"/>
</StackPanel>
</ScrollViewer>
</Grid>
if you don't want to use Multiple columns you have to use canvas where you can control which element comes on top by changing ZIndex Property.