I am not familiar with Office for Mac but, I would 'assume' it is somewhat similar to the standard Office software.

In any case, if your version has an "Insert" ribbon, go to the "Text" portion of that ribbon and select "Date & Time". Select the date/time option of your choice and then check the "Update Automatically" checkbox in lower right-hand portion of the drop-down menu. Use this insert option at each place you desire within your document and you will no longer have to search/replace. It will update automatically each time you "save" your document.