I assume that you are using automatic column population to populate your grid. If you want to hide a column, then you can't really do this - you need to explicitly set the column information manually. To do this, use something like this:
<dg:DataGrid x:Name="dgFollowUp" AutoGenerateColumns="False">
<dg:DataGrid.Columns>
<dg:DataGridTextColumn Binding="{Binding Column1}" Header="Column 1" />
<dg:DataGridTextColumn Binding="{Binding Column2}" Header="Column 1" />
</dg:DataGrid.Columns>
</dg:DataGrid AutoGenerateColumns="False">