I started with
Sub CopyRows()
    Application.ScreenUpdating = False
    Dim bottomA As Integer
    bottomA = Sheets("Sheet1").Range("E" & Rows.Count).End(xlUp).Row
    Dim rng As Range
    For Each rng In Sheets("Sheet1").Range("E2:E" & bottomA)
        If rng = "Finished" Then
            rng.EntireRow.Copy Sheets("Sheet4").Cells(Rows.Count, "A").End(xlUp).Offset(1, 0)
        End If
    Next rng
    Application.CutCopyMode = False
End Sub
But cannot figure out to implement to delete rows in Sheet1 once they are copied.