<Window x:Class="WpfApp.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:model="clr-namespace:WpfApp.Models"
        Title="MainWindow" Height="350" Width="525">
    
    <Window.DataContext>
        <model:MainWindowModel />
    </Window.DataContext>

    <DataGrid Name="gdUsers" ItemsSource="{Binding Items, Mode=TwoWay}" CanUserDeleteRows="False" AutoGenerateColumns="False" PreviewKeyDown="DataGrid_PreviewKeyDown">
        <DataGrid.Columns>
            <DataGridTextColumn Binding="{Binding UserId}" Width="Auto" Header="Код" IsReadOnly="True" />
            <DataGridTextColumn Binding="{Binding UserName}" Width="SizeToHeader" Header="Название" IsReadOnly="True" />
        </DataGrid.Columns>
    </DataGrid>
</Window>

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }

    private void DataGrid_PreviewKeyDown(object sender, KeyEventArgs e)
    {
        if (e.Key == Key.Delete)
        {
            if (MessageBox.Show("Удалить?", "", MessageBoxButton.YesNo, MessageBoxImage.Question) == MessageBoxResult.Yes)
            {
                (DataContext as MainWindowModel).Remove(gdUsers.SelectedItem as User);
            }
        }
    }
}

public class MainWindowModel: INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;

    private void NotifyPropertyChanged(string info)
    {
        if (PropertyChanged != null)
        {
            PropertyChanged(this, new PropertyChangedEventArgs(info));
        }
    }

    private ObservableCollection<User> items;
    
    public ObservableCollection<User> Items
    {
        get
        {
            return items;
        }
        set
        {
            items = value;
            NotifyPropertyChanged("Items");
        }
    }

    public MainWindowModel()
    {
        Items = new ObservableCollection<User>(Enumerable.Range(1, 10).Select(d => new User { UserId = d, UserName = "User " + d }));
    }

    public void Remove(User CurrentUser)
    {
        Items = new ObservableCollection<User>(Items.Where(d => d != CurrentUser));
    }
}

public class User
{
    public int UserId { get; set; }
    public string UserName { get; set; }
}