public void Delete()

public async Task DeletingARowOrFeature()
{
  string message = String.Empty;
  bool deletionResult = false;

  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
    using (Table enterpriseTable = geodatabase.OpenDataset<Table>("LocalGovernment.GDB.piCIPCost"))
    {
      //var geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(uri)) for a File GDB
      //
      //var shapeFileConnPath = new FileSystemConnectionPath(uri, FileSystemDatastoreType.Shapefile);
      //var shapefile = new FileSystemDatastore(shapeFileConnPath);
      //var table = shapefile.OpenDataset<Table>(strShapeFileName); for a Shape file

      EditOperation editOperation = new EditOperation();
      editOperation.Callback(context =>
      {
        QueryFilter openCutFilter = new QueryFilter { WhereClause = "ACTION = 'Open Cut'" };

        using (RowCursor rowCursor = enterpriseTable.Search(openCutFilter, false))
        {
          while (rowCursor.MoveNext())
          {
            using (Row row = rowCursor.Current)
            {
              // In order to update the Map and/or the attribute table. Has to be called before the delete.
              context.Invalidate(row);

              row.Delete();
            }
          }
        }
      }, enterpriseTable);

      try
      {
        deletionResult = editOperation.Execute();
        if (!deletionResult) message = editOperation.ErrorMessage;
      }
      catch (GeodatabaseException exObj)
      {
        message = exObj.Message;
      }
    }
  });

  if (!string.IsNullOrEmpty(message))
    MessageBox.Show(message);
}