Word doesn't have a built in feature for this, so you need a macro.
Something like

Sub splitandsave()

Dim i As Integer
Dim intDocumentCount As Integer
Dim strDocumentName As String
Dim oDoc As Document
Dim oPrintDoc As Document
Set oDoc = ActiveDocument
intDocumentCount = oDoc.Sections.Count
For i = 1 To intDocumentCount
 oDoc.Sections.First.Range.Cut
 Set oPrintDoc = Documents.Add
 With oPrintDoc
   .Content.Paste
   If .Sections.Count > 1 Then
     .Sections(2).PageSetup.SectionStart = wdSectionContinuous
   End If
' change the following line to put the documents in the path you want with
the names you want.
   .SaveAs "doc" & CStr(i) & ".doc"
   .Close Savechanges:=False
 End With
Next
Set oPrintDoc = Nothing
Set oDoc = Nothing
End Sub

--
Peter Jamieson
MS Word MVP