If you come across the need to delete a specific member of a Partitioned dataset and you want to do it via batch job, then you can use IDCAMS for the effect:
//DELETE EXEC PGM=IDCAMS
//SYSPRINT DD SYSOUT=*
//SYSIN DD *
In the above example member MEMBER1 of the partitioned dataset USER1.PDS.EXAMPLE will be deleted.