Try setting the DisplayAlerts to False (then back to true if that is what you want as the default setting.
Application.DisplayAlerts = False
On Error Resume Next
ThisWorkBook.Sheets("Process Map").Delete
On Error Goto 0
Application.DisplayAlerts = True
ThisWorkbook.Sheets.Add.Name = "Process Map"
Or without error handling:
Application.DisplayAlerts = False
ThisWorkBook.Sheets("Process Map").Delete
Application.DisplayAlerts = True
ThisWorkbook.Sheets.Add.Name = "Process Map"