Unfortunately (or fortunately) Word does not work like excel and there the keybinding follows different logic. Thus, in Word, you should try something like this, to bind Ctrl + S. The idea is that on openning of the file you tell the application to bind Ctrl + S to the SaveMe
Sub.
Option Explicit
Private Sub Document_Open()
With Application
.CustomizationContext = ThisDocument
.KeyBindings.Add KeyCode:=BuildKeyCode(wdKeyControl, wdKeyS), KeyCategory:=wdKeyCategoryCommand, Command:="SaveMe"
End With
End Sub
Public Sub SaveMe()
MsgBox "User Saved"
End Sub
Put the code in ThisDocument
:

Until now, it works this way only for Ctrl+S. If you go for the Save through the menu, it will not follow this logic. This is what you should do then:
For the general solution, follow these instructions:
I. Create a clsWord
and put the following code inside:
Option Explicit
Public WithEvents appWord As Word.Application
Private Sub appWord_DocumentBeforeSave(ByVal Doc As Document, SaveAsUI As Boolean, Cancel As Boolean)
Call SaveMe
End Sub
II. Change the code in ThisDocument
to this:
Option Explicit
Dim myWord As New clsWord
Private Sub Document_Open()
With Application
.CustomizationContext = ThisDocument
.KeyBindings.Add KeyCode:=BuildKeyCode(wdKeyControl, wdKeyS), _
KeyCategory:=wdKeyCategoryCommand, Command:="SaveMe"
End With
Set myWord.appWord = Word.Application
End Sub
III. In a module:
Option Explicit
Public Sub SaveMe()
MsgBox "User Saved"
End Sub
Parts of the ideas are taken from the MSDN here - https://msdn.microsoft.com/en-us/library/office/ff838299.aspx But the code there was not complete :)