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);
}