You've got two problems:
You're trying to set VerticalScrollModeProperty to something that doesn't change the scroll mode - "ScrollBarVisibility.Disabled" changes the scrollbar's visibility, but it doesn't disable scrolling. Instead, you'll want to use "ScrollMode.Disabled".
VerticalScrollModeProperty is a property which can only be retrieved with a getter (element.getValue(...)), and changed with a setter (element.setValue(...)). Some properties require you to do this instead of accessing them directly (which is what you were trying to do with the syntax ScrollViewer.VerticalScrollModeProperty = someValue). In the future, if you get the error you got above, chances are your next step is to try using getValue() and setValue() for that property instead.
So! If you want to disable vertical scrolling on the C# side of things (as you were trying to do above), use this:
editBoxName.setValue(VerticalScrollModeProperty, ScrollMode.Disabled);
If you're in the stylesheet (like StandardStyles.xaml) and want to set this property there instead of doing so programmatically (say you want multiple RichEditBox elements with scrolling disabled), try this:
<Style x:Key="styleName" TargetType="RichEditBox">
<Setter Property="ScrollViewer.VerticalScrollMode" Value="Disabled" />
<!-- your other RichEditBox properties can go here, if you'd like -->
</Style>
Final note - if you go the stylesheet route, to to get your RichEditBox correctly using that style ("styleName"), you'll want to do the following in the XAML where you instantiate your RichEditBox:
<RichEditBox x:Name="myEditBox" Style="{StaticResource ResourceKey=styleName}" />