In order to break a link, you will need to delete the relationship record.
Warning: While deleting information is always something to be extremely cautious about - the API will not allow you to delete anything that cannot normally be deleted through the front end of Raiser's Edge.
 
Tip: The field IS_PRIMARY must be set to false before deleting an reciprocal relationship. For example:  Cindividual2.Fields(INDIVIDUAL2_fld_IS_PRIMARY) = False

Public Sub DeleteRelationship()
   Dim oRels As CIndividuals2
   Set oRels = New CIndividuals2
   'Load the individuals for the constituent with and id of 280
   oRels.Init REApplication.SessionContext, 280
   
   Dim oRel As CIndividual2
   Dim lid As Long
   
   'Loop through the individuals to find the one to delete
   For Each oRel In oRels
       MsgBox oRel.Fields(INDIVIDUAL2_fld_NAME)
       If oRel.Fields(INDIVIDUAL2_fld_LAST_NAME) = "Jones" Then
       'Get the ID of the indiviual to be deleted
       lid = oRel.Fields(INDIVIDUAL2_fld_ID)
       
       Dim oRelDel As CIndividual2
       Set oRelDel = New CIndividual2
       oRelDel.Init REApplication.SessionContext
      
       'Load the individual to be deleted
       oRelDel.Load lid
           'Setting Delete to false will not remove the reciprocal
           'Setting Delete to true will remove the relationship from the reciprocal record
           oRelDel.Delete
           MsgBox "Deleted"
          
           oRelDel.CloseDown
           Set oRelDel = Nothing
       End If
      
      oRel.CloseDown
   Next oRel
  
   'Cleanup
   oRels.CloseDown
   Set oRels = Nothing
  
   Set oRel = Nothing
End Sub

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