Вам необходимо отредактировать ControlTemplate для MenuItem.
Скопируйте его из GitHub и избавьтесь от полей элемента Grid в ScrollViewer в Popup:
<Menu Name="mnuMain" Background="orange" Height="30" Padding="0">
<Menu.Resources>
<Style TargetType="{x:Type MenuItem}" BasedOn="{x:Null}">
<Setter Property="Padding" Value="24 0 24 0"></Setter>
<Setter Property="OverridesDefaultStyle" Value="True"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type MenuItem}">
<ControlTemplate.Resources>
<Style TargetType="{x:Type materialDesign:PackIcon}" >
<Setter Property="Width" Value="16" />
<Setter Property="Height" Value="16" />
</Style>
</ControlTemplate.Resources>
<Grid ClipToBounds="True">
<Border x:Name="templateRoot"
BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
Background="{TemplateBinding Background}"
SnapsToDevicePixels="True"/>
<Border x:Name="BackgroundRoot"
BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
Background="{TemplateBinding Foreground, Converter={StaticResource BrushRoundConverter}}"
SnapsToDevicePixels="True"
Opacity="0"/>
<materialDesign:Ripple Background="Transparent"
HorizontalContentAlignment="Stretch" VerticalContentAlignment="Stretch"
Focusable="False"
Feedback="{TemplateBinding Foreground, Converter={StaticResource BrushRoundConverter}}">
<Grid Height="{TemplateBinding Height}" Background="Transparent">
<Grid VerticalAlignment="Center"
Background="Transparent"
Margin="{TemplateBinding Padding}">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto" SharedSizeGroup="IconGroup"/>
<ColumnDefinition Width="*" SharedSizeGroup="HeaderGroup"/>
<ColumnDefinition Width="*"/>
</Grid.ColumnDefinitions>
<Grid x:Name="IconWrapper" Visibility="Visible" Width="40">
<ContentPresenter x:Name="Icon"
Content="{TemplateBinding Icon}"
ContentSource="Icon"
HorizontalAlignment="Left" VerticalAlignment="Center"
Height="16" Width="16"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"/>
</Grid>
<Grid x:Name="GlyphWrapper" Visibility="Collapsed" Width="40">
<Viewbox x:Name="GlyphPanel"
Width="16" Height="16"
HorizontalAlignment="Left"
Margin="0" Visibility="Collapsed" VerticalAlignment="Center"
FlowDirection="LeftToRight">
<Canvas Width="24" Height="24">
<Path Data="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"
x:Name="Glyph"
Fill="{TemplateBinding Foreground}" FlowDirection="LeftToRight" />
</Canvas>
</Viewbox>
</Grid>
<Grid Grid.Column="1">
<ContentPresenter x:Name="BoldHeaderPresenter"
Visibility="Hidden"
TextBlock.FontWeight="Bold"
ContentTemplate="{TemplateBinding HeaderTemplate}"
Content="{TemplateBinding Header}"
ContentStringFormat="{TemplateBinding HeaderStringFormat}"
ContentSource="Header"
RecognizesAccessKey="True"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
VerticalAlignment="Center"/>
<ContentPresenter x:Name="HeaderPresenter"
ContentTemplate="{TemplateBinding HeaderTemplate}"
Content="{TemplateBinding Header}"
ContentStringFormat="{TemplateBinding HeaderStringFormat}"
ContentSource="Header"
RecognizesAccessKey="True"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
VerticalAlignment="Center"/>
</Grid>
<Grid x:Name="InputGestureTextWrapper"
Grid.Column="2"
Visibility="Collapsed">
<TextBlock Visibility="{TemplateBinding InputGestureText, Converter={StaticResource StringIsEmptyVisibilityConverter}}"
Margin="16 0 0 0"
VerticalAlignment="Center" HorizontalAlignment="Right"
Text="{TemplateBinding InputGestureText}"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
Foreground="{TemplateBinding Foreground}"/>
</Grid>
<Grid x:Name="SubBlock"
Grid.Column="2"
Visibility="Collapsed"
Margin="16 0 0 0">
<Path Width="5" Height="10"
Stretch="Uniform"
HorizontalAlignment="Right"
VerticalAlignment="Center"
Data="M0,16 L8,8 L0,0 Z"
Fill="{TemplateBinding Foreground}"
SnapsToDevicePixels="False"/>
</Grid>
</Grid>
</Grid>
</materialDesign:Ripple>
<Popup x:Name="PART_Popup"
AllowsTransparency="True"
Focusable="False"
IsOpen="{Binding IsSubmenuOpen, RelativeSource={RelativeSource TemplatedParent}}"
PopupAnimation="Slide"
Placement="Bottom"
CacheMode="{Binding RelativeSource={RelativeSource Self}, Path=(materialDesign:ShadowAssist.CacheMode)}">
<Border x:Name="SubMenuBorder"
Background="{Binding Path=Background, RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=MenuBase}}"
Effect="{DynamicResource MaterialDesignShadowDepth1}"
CornerRadius="2">
<Border Background="Transparent">
<ScrollViewer x:Name="SubMenuScrollViewer" Style="{DynamicResource {ComponentResourceKey ResourceId=MenuScrollViewer, TypeInTargetAssembly={x:Type FrameworkElement}}}">
<Grid RenderOptions.ClearTypeHint="Enabled" Margin="0">
<Canvas HorizontalAlignment="Left" Height="0" VerticalAlignment="Top" Width="0">
<Rectangle x:Name="OpaqueRect"
Fill="{Binding Background, ElementName=SubMenuBorder}"
Height="{Binding ActualHeight, ElementName=SubMenuBorder}"
Width="{Binding ActualWidth, ElementName=SubMenuBorder}"/>
</Canvas>
<ItemsPresenter x:Name="ItemsPresenter"
KeyboardNavigation.DirectionalNavigation="Cycle"
Grid.IsSharedSizeScope="True"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
KeyboardNavigation.TabNavigation="Cycle"/>
</Grid>
</ScrollViewer>
</Border>
</Border>
</Popup>
</Grid>
<ControlTemplate.Triggers>
<Trigger Property="Role" Value="SubmenuHeader">
<Setter TargetName="SubBlock" Property="Visibility" Value="Visible" />
<Setter TargetName="PART_Popup" Property="Placement" Value="Right" />
<Setter Property="Height" Value="32"/>
<Setter TargetName="BoldHeaderPresenter" Property="Visibility" Value="Collapsed"/>
</Trigger>
<Trigger Property="Role" Value="SubmenuItem">
<Setter Property="Height" Value="32"/>
<Setter TargetName="InputGestureTextWrapper" Property="Visibility" Value="Visible"/>
<Setter TargetName="BoldHeaderPresenter" Property="Visibility" Value="Collapsed"/>
</Trigger>
<Trigger Property="Role" Value="TopLevelHeader">
<Setter Property="Grid.IsSharedSizeScope" Value="True"/>
<Setter Property="Padding" Value="16 0"/>
<Setter Property="Height" Value="48"/>
<Setter TargetName="templateRoot" Property="CornerRadius" Value="2"/>
<Setter TargetName="BackgroundRoot" Property="CornerRadius" Value="2"/>
</Trigger>
<Trigger Property="Role" Value="TopLevelItem">
<Setter Property="Padding" Value="16 0"/>
<Setter Property="Height" Value="48"/>
<Setter TargetName="templateRoot" Property="CornerRadius" Value="2"/>
<Setter TargetName="BackgroundRoot" Property="CornerRadius" Value="2"/>
</Trigger>
<MultiTrigger>
<MultiTrigger.Conditions>
<Condition Property="Role" Value="TopLevelHeader"/>
<Condition Property="IsSubmenuOpen" Value="True"/>
</MultiTrigger.Conditions>
<MultiTrigger.Setters>
<Setter TargetName="HeaderPresenter" Property="TextBlock.FontWeight" Value="Bold"/>
</MultiTrigger.Setters>
</MultiTrigger>
<Trigger Property="HasDropShadow" SourceName="PART_Popup" Value="True">
<Setter TargetName="SubMenuBorder" Property="Margin" Value="5"/>
</Trigger>
<Trigger Property="IsSuspendingPopupAnimation" Value="True">
<Setter Property="PopupAnimation" TargetName="PART_Popup" Value="None"/>
</Trigger>
<Trigger Property="Icon" Value="{x:Null}">
<Setter Property="Visibility" TargetName="IconWrapper" Value="Collapsed"/>
</Trigger>
<Trigger Property="IsChecked" Value="True">
<Setter Property="Visibility" TargetName="GlyphPanel" Value="Visible"/>
</Trigger>
<Trigger Property="IsCheckable" Value="True">
<Setter Property="Visibility" TargetName="GlyphWrapper" Value="Visible"/>
<Setter Property="Visibility" TargetName="IconWrapper" Value="Collapsed"/>
</Trigger>
<Trigger Property="IsHighlighted" Value="True">
<Setter TargetName="BackgroundRoot" Property="Opacity" Value="0.13"/>
</Trigger>
<Trigger Property="IsEnabled" Value="False">
<Setter Property="Opacity" Value=".56"/>
</Trigger>
<Trigger Property="CanContentScroll" SourceName="SubMenuScrollViewer" Value="False">
<Setter Property="Canvas.Top" TargetName="OpaqueRect" Value="{Binding VerticalOffset, ElementName=SubMenuScrollViewer}"/>
<Setter Property="Canvas.Left" TargetName="OpaqueRect" Value="{Binding HorizontalOffset, ElementName=SubMenuScrollViewer}"/>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</Menu.Resources>
<MenuItem Name="File" Height="30" Header="File">
<MenuItem Name="Open" Header="Open" Background="{StaticResource DefaultContent}" Margin="0"/>
<MenuItem Name="Close" Header="Close" Background="{StaticResource DefaultContent}"/>
</MenuItem>
<MenuItem Name="Edit" Height="30" Header="Edit">
<MenuItem Name="Copy" Header="Copy" Background="{StaticResource DefaultContent}" />
<MenuItem Name="Paste" Header="Paste" Background="{StaticResource DefaultContent}"/>
</MenuItem>
</Menu>