What are the process instances that we need to delete automatically as soon as we execute the process ?

Is the question about a specific issue or generic?

Data management in processes is mostly about memory consumption, the Appian exec engines will not slow down just because of many active/completed process instances.

What DB do you mean? The relational DBs integrated to Appian do not care about processes.

Check your health check.  It will show you what you need to know.  If you have processes that are taking up huge chunks of your memory, you can cut down on those specific ones.  I would first see if there's a way to more efficiently do the same work.  See if you can get the stuff you need with a more efficient query, smaller CDT, etc.  If that doesn't cut it, you can make them archive sooner, or if you need to archive immediately. 

However, archiving sooner hurts your ability to triage incidents and rectify them by developer modifications to in-flight processes.  The more you archive, the less you can fix.  So don't do it unless the improved performance is needed and you can afford to have them archived. If everything is in the green don't do anything.  If it's in the yellow or red, get it in the green then don't do more.

If your DB needs better performance, don't fix Appian.  Fix your DB.  Optimizing your VIEWs or an Index or two can make a world of difference.