Try: Put DataGrid inside ScrollViewer tag then set Height, Width etc. Code sample as shown below.
<Grid>
<GroupBox>
<StackPanel Orientation="Horizontal" >
<ScrollViewer Width="500" ScrollViewer.VerticalScrollBarVisibility="Auto" Foreground="Red">
<DataGrid HorizontalAlignment="Center" AutoGenerateColumns="False" >
<DataGrid.Columns>
</DataGrid.Columns>
</DataGrid>
</ScrollViewer>
</StackPanel>
</GroupBox>
</Grid>
In case of issue let us know.