Below C# code will help you to copy the existing table using Office interop assebly:
using Microsoft.Office.Interop.Word;
Word.Range range = table.Range;
range.Copy();
Word.Range rng = table.Range;
rng.SetRange(table.Range.End, table.Range.End);
Word.Table tableCopy = document.Tables.Add(rng, 1, 1, ref missing, ref missing);
tableCopy.Range.Paste();