You can replace the formula after copying (making sure that the new references will be valid locally). This is what I would do in VBA:

Sheet1.Range("A1").Formula2 = "=" & Mid(Sheet1.Range("A1").Formula2, InStr(Sheet1.Range("A1").Formula2, "'!") + 2)

Do you need help converting to C# (I don't have access to VSTO at work, where I am, but can help later)?