public void ClearRedoCategory( 
   string category
)

// in order to find a dockpane you need to know it's DAML id
var pane = FrameworkApplication.DockPaneManager.Find("esri_core_contentsDockPane");

// get the undo stack
OperationManager manager = pane.OperationManager;
if (manager != null)
{
  // undo an operation
  if (manager.CanUndo)
    await manager.UndoAsync();

  // redo an operation
  if (manager.CanRedo)
    await manager.RedoAsync();

  // clear the undo and redo stack of operations of a particular category
  manager.ClearUndoCategory("Some category");
  manager.ClearRedoCategory("Some category");
}