BEST method TO delete all record?

It looks to me like there's a problem with your LINQ query:

var deleteRecord1 = _service.GetAllDutyPointStatus().Where(x => x.Date == dt && x.Sector_Id == sectorId).Count(); 

All this does is count the records to be deleted - it doesn't return references to the records themselves. 

Also it's never going to be null as it's an int.

If the _service.DeleteDutyPointStatus method takes a 'scalar' variable as a parameter (i.e. not an array or other collection but a single record reference), you could try instead:

var deleteRecord1 = _service.GetAllDutyPointStatus().Where(x => x.Date == dt && x.Sector_Id == sectorId); 

if (deleteRecord1.Count() > 0)        
{              
  foreach(var record in deleteRecord1)
  {
    _service.DeleteDutyPointStatus(record);            
  }
}        
else            
{                
  MsgLitteral.ShowNotificationInline("No Record Found!.", true);              
}