Declare index is mainly used to write the source page context into an index class data instance. If the source class property is updated then the index class property is also updated by PRPC. Similarly addition and deletion works for declare index. Kindly share your business scenario or problem statement to provide more accurate solution.
Pega advise to avoid Property-Set or Obj-Save method of Index - derived classes in order to restrict multiple update of a same instance stored in Index table. Index class is mainly used for Declare Index and thus any instance of this class should be updated or added via declare index.
In your requirement you can try with normal OOTB delete method but the purpose of declare index is to expose the embedded data to ease the access and make it much faster during reporting.