How do I keep the WPF GridSplitter from changing the size of my Grid?

Try changing your Width's to star sizes. This will cause the splitter to only resize the columns between which it sits, so not sure if this is your desired behavior. However, with star sizes, the content will not grow beyond the bounds of the window.

<Grid>
    <Grid.ColumnDefinitions>
        <ColumnDefinition Width="2*" MinWidth="100" />
        <ColumnDefinition Width="Auto" />
        <ColumnDefinition Width="*" MinWidth="50" />
        <ColumnDefinition Width="2*" MinWidth="100" />
        <ColumnDefinition Width="Auto" />
        <ColumnDefinition Width="3*" MinWidth="150" />
    </Grid.ColumnDefinitions>
    <GridSplitter 
        ResizeDirection="Columns"
        Grid.Column="1"
        Grid.RowSpan="8"
        HorizontalAlignment="Center"
        VerticalAlignment="Stretch"
        Width="2"
        Margin="0,5,0,5"
        Panel.ZIndex="1"/>
    ...
</Grid>

If your Window is resized so its Width is less than the sum of your columns' MinWidths, you'll see the columns cut off, but otherwise I can't reproduce your problem:

<Window xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:sys="clr-namespace:System;assembly=mscorlib"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition MinWidth="150" Width="*"/>
            <ColumnDefinition Width="Auto"/>
            <ColumnDefinition MinWidth="400" Width="*"/>
        </Grid.ColumnDefinitions>
        <GridSplitter
            Width="2"
            Grid.Column="1"
            HorizontalAlignment="Center"
            Margin="0,5,0,5"
            Panel.ZIndex="1"
            VerticalAlignment="Stretch"
            ResizeBehavior="BasedOnAlignment"
            ResizeDirection="Columns"/>
        <Grid Grid.Column="0">
            <Border Background="Red" Margin="5"/>
        </Grid>
        <Grid Grid.Column="2">
            <Grid.ColumnDefinitions>
                <ColumnDefinition MinWidth="150" Width="*"/>
                <ColumnDefinition Width="Auto"/>
                <ColumnDefinition MinWidth="200" Width="*"/>
            </Grid.ColumnDefinitions>
            <GridSplitter
                Width="2"
                Grid.Column="1"
                HorizontalAlignment="Center"
                Margin="0,5,0,5"
                Panel.ZIndex="1"
                VerticalAlignment="Stretch"
                ResizeBehavior="PreviousAndNext"
                ResizeDirection="Columns"/>
            <Grid Grid.Column="0">
                <Border Background="Green" Margin="5"/>
            </Grid>
            <Grid Grid.Column="2">
                <Border Background="Blue" Margin="5"/>
            </Grid>
        </Grid>
    </Grid>
</Window>

Expanding the red column, it will only expand until the right column reaches its MinWidth of 400, it won't boot it off the page.

It's possible you're setting other properties of the Window or the outermost Grid that would cause this behavior...

It works for me without any additional code when there are no Columns with Auto Width between the splitters, i.e.:

<Grid >
<Grid.ColumnDefinitions>
    <ColumnDefinition Width="20*" MinWidth="50" MaxWidth="500" />
    <ColumnDefinition Width="Auto"/> <!-- Remove such columns /-->
    <ColumnDefinition Width="100*" MinWidth="850"/>
    <ColumnDefinition Width="30*" MinWidth="50" MaxWidth="800" />
</Grid.ColumnDefinitions>
...
<GridSplitter HorizontalAlignment="Right" Width="3"/>
...
<GridSplitter Grid.Column="3" HorizontalAlignment="Left" Width="3" />
<!-- Assign Grid.Column to 2 if you remove the auto width column /-->
...
</Grid>

Otherwise the grid will be resizable.