There is no automated way to delete and then purge incidents from the system.
Unless you spend a large amount of time figuring out the DB schema (I've done some digging and it isn't easy), doing any kind of SQL operation to delete incidents is a very dangerous operation. If it screws up your system you are on your own to fix it as support won't touch it.
Understand that the schema is auto generated and there is no guarantee it will be the same from release to release, major or minor.
The sysetm does a nightly purge of all deleted incidents. If you delete a bunch of incidents and check the DB the next day, you are NOT going to see any changes. Oracle does not return disk space to the OS.
The only way to "recover" the space (Sorry Mark!) is to stop the DLP system and use DB tools to export, delete the tables and then import the tables. This forces a reorganization of the data, compacts it and then only allocates the space needed.
I vaguely recall that there is an online way to do this, but I'll leave that to the DBAs to work out.
JGT