I don't know of an elegant way to do this, but this works --

1. Select the text you want to copy.
2. Press Alt-F11 to switch to VBA.
3. In the Immediate window (bottom right), type:
Selection.FormattedText.ListFormat.ConvertNumbersToText
4. Copy your text.
5. Press Undo to reverse the conversion to plain text.

If you often need to copy text from one document and paste it into another
document with the numbering unchanged, you could use a macro to perform the
copying steps that are required. If you assign the macro to a toolbar button
or a keyboard shortcut, it is as fast to execute as a normal copy.

You can use the macro below. The actions performed by the macro correspond
to the steps described by Jezebel in the previous post, i.e. the macro:
- changes automatically generated numbers (in headings, lists) in the
selected text to normal text so that the numbers do not change when pasted
into another document
- copies the text
- undoes the change in the original document

If you use the macro to copy the desired text, you only need to go to the
destination document and select paste (Ctrl+V).

Note:
If you reapply a numbered style to a paragraph that has been changed by the
macro, the paragraph will have two numbers: an automatically applied number
plus the "old" number that was converted to normal text (must be corrected
manually).
It is always a good idea to create a backup copy of your original document
in case problems should occur.

The macro:

Sub CopySelection_PreserveNumbersWhenPasting()
   Dim oRange As Range
   
   Set oRange = Selection.Range
   'Unlink heading numbers in range
   With oRange
       .ListFormat.ConvertNumbersToText wdNumberParagraph
       .Copy
   End With
   'Undo the change
   ActiveDocument.Undo
   
   Set oRange = Nothing

End Sub

Another method is to copy the text and then, on the Edit menu, click
Paste Special. Choose to paste as "Unformatted Text."