You could edit a copy of the button style and make the clipping as well as the border inside the new style for the button, this way you can even customize the different states of the button when the user interacts with it.
Something like this:
<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="ASD_Answer001.MainPage" d:DesignWidth="513" d:DesignHeight="298">
<UserControl.Resources>
<Style x:Key="ArrowButton" TargetType="Button">
<Setter Property="Background" Value="#FF1F3B53"/>
<Setter Property="Foreground" Value="#FF000000"/>
<Setter Property="Padding" Value="3"/>
<Setter Property="BorderThickness" Value="1"/>
<Setter Property="BorderBrush">
<Setter.Value>
<LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
<GradientStop Color="#FFA3AEB9" Offset="0"/>
<GradientStop Color="#FF8399A9" Offset="0.375"/>
<GradientStop Color="#FF718597" Offset="0.375"/>
<GradientStop Color="#FF617584" Offset="1"/>
</LinearGradientBrush>
</Setter.Value>
</Setter>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="Button">
<Grid>
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
<VisualStateGroup.Transitions>
<VisualTransition GeneratedDuration="0:0:0.2">
<VisualTransition.GeneratedEasingFunction>
<CircleEase EasingMode="EaseOut"/>
</VisualTransition.GeneratedEasingFunction>
</VisualTransition>
</VisualStateGroup.Transitions>
<VisualState x:Name="Normal"/>
<VisualState x:Name="MouseOver">
<Storyboard>
<ColorAnimation Duration="0" To="#FF6DB7DA" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[0].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#F99FD7EF" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#E5A5C1CE" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[2].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#C6FFFFFF" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[3].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<DoubleAnimation Duration="0" To="0.322" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Offset)" Storyboard.TargetName="path" d:IsOptimized="True"/>
</Storyboard>
</VisualState>
<VisualState x:Name="Pressed">
<Storyboard>
<ColorAnimation Duration="0" To="#FFF9FEB0" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[0].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#F9FEFFEB" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#E5D9E16C" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[2].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
</Storyboard>
</VisualState>
<VisualState x:Name="Disabled">
<Storyboard>
<DoubleAnimation Duration="0" To=".55" Storyboard.TargetProperty="Opacity" Storyboard.TargetName="DisabledVisualElement"/>
<ColorAnimation Duration="0" To="#FFFEFEFE" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[0].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#F9FFFFFF" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[1].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
<ColorAnimation Duration="0" To="#E5E1E1E1" Storyboard.TargetProperty="(Shape.Fill).(GradientBrush.GradientStops)[2].(GradientStop.Color)" Storyboard.TargetName="path" d:IsOptimized="True"/>
</Storyboard>
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualStateGroup.Transitions>
<VisualTransition GeneratedDuration="0:0:0.2">
<VisualTransition.GeneratedEasingFunction>
<CircleEase EasingMode="EaseOut"/>
</VisualTransition.GeneratedEasingFunction>
</VisualTransition>
</VisualStateGroup.Transitions>
<VisualState x:Name="Focused">
<Storyboard>
<DoubleAnimation Duration="0" To="1" Storyboard.TargetProperty="Opacity" Storyboard.TargetName="FocusVisualElement"/>
<DoubleAnimation Duration="0" To="4" Storyboard.TargetProperty="(Shape.StrokeThickness)" Storyboard.TargetName="path" d:IsOptimized="True"/>
</Storyboard>
</VisualState>
<VisualState x:Name="Unfocused"/>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Path x:Name="path" Data="M30,26.5 L358,24.5 L589.64996,219.49998 L394,404.5 L30,414.5 L178.28333,226.3421 z" Margin="8,8,11,8" Stretch="Fill" UseLayoutRounding="False" Stroke="Black" StrokeThickness="2" d:LayoutOverrides="VerticalAlignment">
<Path.Fill>
<LinearGradientBrush EndPoint="0.699999988079071,1" StartPoint="0.699999988079071,0">
<GradientStop Color="#FFB0E5FE" Offset="0"/>
<GradientStop Color="#F9EBF9FF" Offset="0.375"/>
<GradientStop Color="#E56CBCE1" Offset="0.625"/>
<GradientStop Color="#C6FFFFFF" Offset="1"/>
</LinearGradientBrush>
</Path.Fill>
</Path>
<ContentPresenter x:Name="contentPresenter" ContentTemplate="{TemplateBinding ContentTemplate}" Content="{TemplateBinding Content}" HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}" Margin="{TemplateBinding Padding}" VerticalAlignment="{TemplateBinding VerticalContentAlignment}"/>
<Rectangle x:Name="DisabledVisualElement" Fill="#FFFFFFFF" IsHitTestVisible="false" Opacity="0" RadiusY="3" RadiusX="3"/>
<Rectangle x:Name="FocusVisualElement" IsHitTestVisible="false" Margin="1" Opacity="0" RadiusY="2" RadiusX="2" Stroke="#FF6DBDD1" StrokeThickness="1"/>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</UserControl.Resources>
<Grid x:Name="LayoutRoot" Background="White">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="0.318*"/>
<ColumnDefinition Width="0.329*"/>
<ColumnDefinition Width="0.353*"/>
</Grid.ColumnDefinitions>
<Button Style="{StaticResource ArrowButton}" Height="75" Content="Button 1" Padding="15,1,3,3" VerticalAlignment="Top" Width="138"/>
<Button Style="{StaticResource ArrowButton}" Height="75" Content="Button 2" Padding="15,1,3,3" VerticalAlignment="Top" Grid.Column="1" Width="138"/>
<Button Style="{StaticResource ArrowButton}" Height="75" Content="Button 3" Padding="15,1,3,3" VerticalAlignment="Top" Grid.Column="2" Width="138"/>
</Grid>
</UserControl>