ArcGIS does not support the ability in Oracle to split or merge a partitioned table with a local spatial index.
The following is an example of how one would split an existing partition into two partitions. The current partition is named JAN_2010, and the objective is to split the partition (or months worth of data) into two partitions, where the new partitions will be named JAN_2010_A and JAN_2010_B. This task would typically be performed by the partitioned table's owner.
SQL> ALTER TABLE event_locations SPLIT PARTITION jan_2010 AT (TO_DATE('16-JAN-2010','dd-mon-yyyy'))
INTO (PARTITION jan_2010_a, PARTITION jan_2010_b);
The implementation of the st_spatial_index methods for ODCIIndexSplitPartition and ODCIIndexMergePartition have not been implemented.