I know the accepted answer is quite old, but there is a way to control formatting with AutoGeneratColumns :
First create a function that will trigger when a column is generated :
<DataGrid x:Name="dataGrid" AutoGeneratedColumns="dataGrid_AutoGeneratedColumns" Margin="116,62,10,10"/>
Then check if the type of the column generated is a DateTime and just change its String format to "d" to remove the time part :
private void DataGrid_AutoGeneratingColumn(object sender, DataGridAutoGeneratingColumnEventArgs e)
{
if(YourColumn == typeof(DateTime))
{
e.Column.ClipboardContentBinding.StringFormat = "d";
}
}