use RemoveOverlaps on collection of shapes

My approach - sort of brute force ;) Slow on complex and large number of objects.

Sub Cut()
If ActiveSelectionRange.Count = 0 Then   
    Exit Sub
End If
Dim s, sCopy As Shape, l, temp As Layer, sr As ShapeRange, srCount As Integer, coll As New Collection
ActiveDocument.Unit = cdrMillimeter
ActiveDocument.BeginCommandGroup "Get curves cut ready"
Optimization = True
EventsEnabled = False
ActiveDocument.PreserveSelection = False
Set l = ActiveDocument.ActiveLayer
Set sr = ActiveSelectionRange
Set temp = ActivePage.CreateLayer("Temp")
sr.MoveToLayer temp
For i = 1 To sr.Shapes.Count   
    Set s = sr(i)
    If s.Type <> cdrCurveShape Then s.ConvertToCurves   
    s.Curve.Nodes.All.BreakApart
    s.BreakApart   
    Dim tempSr As ShapeRange
    Set tempSr = ActiveSelectionRange
    coll.Add tempSr       
Next i
For i = 1 To coll.Count
    Set sr = coll(i)   
    For j = 1 To sr.Count   
        Set s = sr(j)
        Set sCopy = s.Duplicate(0, 0)
        sCopy.Outline.width = 1
        sCopy.Outline.ConvertToObject       
        For k = 1 To coll.Count       
            If k <> i Then           
                Dim sr1 As ShapeRange
                Set sr1 = coll(k)               
                srCount = sr1.Count               
                    For h = 1 To srCount                   
                        Set s = sr1(h)
                        Set s = sCopy.Trim(s, True, True)
                        If Not s Is Nothing Then
                            sr1.Add s
                        End If                       
                    Next h                   
                    For m = srCount To 1 Step -1                       
                        sr1(m).Delete
                        sr1.Remove m                   
                    Next m
            End If
        Next k
    sCopy.Delete   
    Next j
Next i
ActiveDocument.ActiveLayer.Shapes.All.MoveToLayer l
temp.Delete
ActiveDocument.ClearSelection
Optimization = False
ActiveDocument.PreserveSelection = True
EventsEnabled = True
Application.Refresh
ActiveDocument.EndCommandGroup
End Sub