The build-in function of Excel would be to ask the user to use PasteSpecial
and copy only the values. However, users tend to not follow that.
What you could do is to create a Change routine that saves the copied values into memory, issue an Undo-Command that will revert the last action, including formatting, and then write back the saved values into the cells. Put the code into the worksheet module of that sheet:
Option Explicit
Private Sub Worksheet_Change(ByVal Target As Range)
Application.EnableEvents = False
' Save modified value
Dim v
ReDim v(1 To Target.Areas.Count)
Dim i As Long
For i = 1 To Target.Areas.Count
v(i) = Target.Areas(i).Value2
Next i
' Undo last action
Application.Undo
' Copy only the values of the last modification
For i = 1 To Target.Areas.Count
Target.Areas(i).Value2 = v(i)
Next i
Application.EnableEvents = True
End Sub